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  • 101. Almér, S.
    et al.
    Mariéthoz, S.
    Morari, M.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Application of model predictive control and analysis of switched systems to the direct voltage control of AC-DC converters2015In: 2009 European Control Conference, ECC 2009, 2015, p. 3593-3598Conference paper (Refereed)
    Abstract [en]

    Recent tools for control and analysis of hybrid systems are applied to an AC-DC converter. The topology poses particularly challenging problems since it is unusually complex and the circuit parameters are such that the dynamic coupling between the AC and DC sides cannot be ignored. The paper proposes a model predictive control scheme for direct voltage control which circumvents the bandwidth limitations associated with classical cascade control. The stability and harmonic properties of the resulting closed loop system are investigated using new tools for the analysis of switched systems.

  • 102.
    Almér, Stefan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Control and Analysis of Pulse-Modulated Systems2008Doctoral thesis, comprehensive summary (Other scientific)
    Abstract [en]

    The thesis consists of an introduction and four appended papers. In the introduction we give an overview of pulse-modulated systems and provide a few examples of such systems. Furthermore, we introduce the so-called dynamic phasor model which is used as a basis for analysis in two of the appended papers. We also introduce the harmonic transfer function and finally we provide a summary of the appended papers.

    The first paper considers stability analysis of a class of pulse-width modulated systems based on a discrete time model. The systems considered typically have periodic solutions. Stability of a periodic solution is equivalent to stability of a fixed point of a discrete time model of the system dynamics.

    Conditions for global and local exponential stability of the discrete time model are derived using quadratic and piecewise quadratic Lyapunov functions. A griding procedure is used to develop a systematic method to search for the Lyapunov functions.

    The second paper considers the dynamic phasor model as a tool for stability analysis of a general class of pulse-modulated systems. The analysis covers both linear time periodic systems and systems where the pulse modulation is controlled by feedback. The dynamic phasor model provides an $\textbf{L}_2$-equivalent description of the system dynamics in terms of an infinite dimensional dynamic system. The infinite dimensional phasor system is approximated via a skew truncation. The truncated system is used to derive a systematic method to compute time periodic quadratic Lyapunov functions.

    The third paper considers the dynamic phasor model as a tool for harmonic analysis of a class of pulse-width modulated systems. The analysis covers both linear time periodic systems and non-periodic systems where the switching is controlled by feedback. As in the second paper of the thesis, we represent the switching system using the L_2-equivalent infinite dimensional system provided by the phasor model. It is shown that there is a connection between the dynamic phasor model and the harmonic transfer function of a linear time periodic system and this connection is used to extend the notion of harmonic transfer function to describe periodic solutions of non-periodic systems. The infinite dimensional phasor system is approximated via a square truncation. We assume that the response of the truncated system to a periodic disturbance is also periodic and we consider the corresponding harmonic balance equations. An approximate solution of these equations is stated in terms of a harmonic transfer function which is analogous to the harmonic transfer function of a linear time periodic system. The aforementioned assumption is proved to hold for small disturbances by proving the existence of a solution to a fixed point equation. The proof implies that for small disturbances, the approximation is good.

    Finally, the fourth paper considers control synthesis for switched mode DC-DC converters. The synthesis is based on a sampled data model of the system dynamics. The sampled data model gives an exact description of the converter state at the switching instances, but also includes a lifted signal which represents the inter-sampling behavior. Within the sampled data framework we consider H-infinity control design to achieve robustness to disturbances and load variations. The suggested controller is applied to two benchmark examples; a step-down and a step-up converter. Performance is verified in both simulations and in experiments.

  • 103.
    Almér, Stefan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Sampled data control of DC-DC convertersArticle in journal (Other academic)
  • 104.
    Almér, Stefan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Dynamic phasor analysis of pulse-modulated systems2007In: Proceedings Of The 46th IEEE Conference On Decision And Control, Vols 1-14, 2007, p. 3938-3945Conference paper (Refereed)
    Abstract [en]

    The paper considers stability analysis of a general class of pulse modulated systems in a phasor dynamic framework. The dynamic phasor model exploits the cyclic nature of the modulation functions by representing the system dynamics in terms of a Fourier series expansion defined over a moving time-window. The contribution of the paper is to show that a special type of periodic Lyapunov function can be used to analyze the system and that the analysis conditions become tractable for computation after truncation. The approach provides a trade-off between complexity and accuracy that includes standard state space averaged models as a special case.

  • 105. Almér, Stefan
    et al.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Dynamic Phasor Analysis Of Pulse-Modulated Systems2012In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 50, no 3, p. 1110-1138Article in journal (Refereed)
    Abstract [en]

    This paper considers stability and harmonic analysis of a general class of pulse-modulated systems. The systems are modeled using the dynamic phasor model, which explores the cyclic nature of the modulation functions by representing the system state as a Fourier series expansion defined over a moving time window. The contribution of the paper is to show that a special type of periodic Lyapunov function can be used to analyze the system and that the analysis conditions become tractable for computation after truncation. The approach provides a trade-off between complexity and accuracy that includes standard state space averaged models as a special case. The paper also shows how the dynamic phasor model can be used to derive a frequency domain input-to-state map which is analogous to the harmonic transfer function.

  • 106.
    Almér, Stefan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Harmonic analysis of pulse-width modulated systems2009In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 45, no 4, p. 851-862Article in journal (Refereed)
    Abstract [en]

    The paper considers the so-called dynamic phasor model as a basis for harmonic analysis of a class switching systems. The analysis covers both periodically switched systems and non-periodic systems where the switching is controlled by feedback. The dynamic phasor model is a powerful tool for exploring cyclic properties of dynamic systems. It is shown that there is a connection between the dynamic phasor model and the harmonic transfer function of a linear time periodic system and this connection is used to extend the notion of harmonic transfer function to describe periodic solutions of non-periodic systems.

  • 107.
    Almér, Stefan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Harmonic Lyapunov functions in the analysis of periodically switched systems2006In: PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2006, p. 2759-2764Conference paper (Refereed)
    Abstract [en]

    The dynamic phasor model of a time-periodic system is used to derive a stability test involving a harmonic Lyapunov function. This reveals a new interpretation of the harmonic Lyapunov function with an appealing time-domain representation. Most importantly, it indicates that the ideas behind the harmonic Lyapunov equation can be generalized to include cyclic switching systems that have different pulse form in each period.

  • 108.
    Almér, Stefan
    et al.
    KTH, Superseded Departments, Mathematics.
    Jönsson, Ulf
    KTH, Superseded Departments, Mathematics.
    Kao, Chung-Yao
    KTH, Superseded Departments, Mathematics.
    Mari, Jorge
    Global stability analysis of DC-DC converters using sampled-data modeling2004In: PROCEEDINGS OF THE 2004 AMERICAN CONTROL CONFERENCE, VOLS 1-6, 2004, p. 4549-4554Conference paper (Refereed)
    Abstract [en]

    The paper presents stability analysis of a class of pulse-width modulated (PWM) systems which incorporates many different DC-DC converters. Two types of pulse-width modulation (digital and analog control) are considered. A procedure is developed for systematic search for Lyapunov functions. The state space is partitioned in such a way that stability is verified if a set of coupled Linear Matrix Inequalities (LMIs) is feasible. Global stability is considered as well as the computation of local regions of attraction.

  • 109.
    Almér, Stefan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Kao, Chung-Yao
    Univ Melbourne, Dept Elect & Elect Engn.
    Mari, Jorge
    GE Global Res, Elect Energy Syst.
    Stability analysis of a class of PWM systems2007In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 52, no 6, p. 1072-1078Article in journal (Refereed)
    Abstract [en]

    This note considers stability analysis of a class of pulsewidth modulated (PWM) systems that incorporates several different switched mode dc-de- converters. The systems of the class typically have periodic solutions. A sampled data model is developed and used to prove stability of these solutions. Conditions for global and local exponential stability are derived using quadratic and piecewise quadratic Lyapunov functions. The state space is partitioned and the stability conditions are verified by checking a set of coupled linear matrix inequalities (LMIs).

  • 110.
    Almér, Stefan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf T.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Dynamic phasor analysis of a class of PWM systems2015In: 2007 European Control Conference, ECC 2007, 2015, p. 1940-1947Conference paper (Refereed)
    Abstract [en]

    The paper makes use of the so-called dynamic phasor model for stability and performance analysis of a class of PWM systems. The dynamic phasor model allows for the state to be represented in the frequency domain where a harmonic Lyapunov function is defined. The analysis covers both periodically switched systems and non-periodic systems where the switching is controlled by feedback.

  • 111.
    Alpsten, Erik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Modeling News Data Flows using Multivariate Hawkes Processes2018Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis presents a multivariate Hawkes process approach to model flows of news data. The data is divided into classes based on the news' content and sentiment levels, such that each class contains a homogeneous type of observations. The arrival times of news in each class are related to a unique element in the multivariate Hawkes process. Given this framework, the massive and complex flow of information is given a more compact representation that describes the excitation connections between news classes, which in turn can be used to better predict the future flow of news data. Such a model has potential applications in areas such as finance and security. This thesis focuses especially on the different bucket sizes used in the discretization of the time scale as well as the differences in results that these imply. The study uses aggregated news data provided by RavenPack and software implementations are written in Python using the TensorFlow package.

    For the cases with larger bucket sizes and datasets containing a larger number of observations, the results suggest that the Hawkes models give a better fit to training data than the Poisson model alternatives. The Poisson models tend to give better performance when models trained on historic data are tested on subsequent data flows. Moreover, the connections between news classes are given to vary significantly depending on the underlying datasets. The results indicate that lack of observations in certain news classes lead to over-fitting in the training of the Hawkes models and that the model ought to be extended to take into account the deterministic and periodic behaviors of the news data flows.

  • 112.
    Alpsten, Gustav
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Samanci, Sercan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Portfolio Protection Strategies: A study on the protective put and its extensions2018Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The need among investors to manage volatility has made itself painfully clear over the past century, particularly during sudden crashes and prolonged drawdowns in the global equity markets. This has given rise to a liquid portfolio insurance market in the form of options, as well as attracted the attention of many researchers. Previous literature has, in particular, studied the effectiveness of the widely known protective put strategy, which serially buys a put option to protect a long position in the underlying asset. The results are often uninspiring, pointing towards few, if any, protective benefits with high option premiums as a main concern. This raises the question if there are ways to improve the protective put strategy or if there are any cost-efficient alternatives that provide a relatively be.er protection. This study extends the previous literature by investigating potential improvements and alternatives to the protective put strategy. In particular, three alternative put spread strategies and one collar strategy are constructed. In addition, a modified protective put this introduced to mitigate the path dependency in a rolling protection strategy.

     

    The results show that no option-based protection strategy can dominate the other in all market situations. Although reducing the equity position is generally more effective than buying options, we report that a collar strategy that buys 5% OTM put options and sells 5% OTM call options has an attractive risk-reward profile and protection against drawdowns. We also show that the protective put becomes more effective, both in terms of risk-adjusted return and tail protection, for longer maturities.

  • 113. Alsafadie, Rabe
    et al.
    Battini, Jean-Marc
    KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
    Hjiaj, Mohammed
    Efficient local formulation for elasto-plastic corotational thin-walled beams2011In: The International Journal for Numerical Methods in Biomedical Engineering, ISSN 2040-7939, Vol. 27, no 4, p. 498-509Article in journal (Refereed)
    Abstract [en]

    A local elasto-plastic formulation, based on a low-order nonlinear strain expression using Bernoulli beam kinematics, is presented in this paper. This element, together with the corotational framework proposed in (Comput. Meth. Appl. Mech. Eng. 2002; 191(17): 1755-1789) can be used to analyze the nonlinear buckling and postbuckling of thin-walled beams with arbitrary cross-section. The formulation captures both the Saint-Venant and warping torsional effects of open cross-sections. Numerical examples show that this local formulation is more efficient than the one proposed in (Comput. Meth. Appl. Mech. Eng. 2002; 191(51):5811-5831) based on a Timoshenko beam assumption.

  • 114.
    Altafi, Nasrin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Lefschetz Properties of Monomial Ideals2018Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis concerns the study of the Lefschetz properties of artinian monomial algebras. An artinian algebra is said to satisfy the strong Lefschetz property if multiplication by all powers of a general linear form has maximal rank in every degree. If it holds for the first power it is said to have the weak Lefschetz property (WLP).

    In the first paper, we study the Lefschetz properties of monomial algebras by studying their minimal free resolutions. In particular, we give an afirmative answer to an specific case of a conjecture by Eisenbud, Huneke and Ulrich for algebras having almost linear resolutions. Since many algebras are expected to have the Lefschetz properties, studying algebras failing the Lefschetz properties is of a great interest. In the second paper, we provide sharp lower bounds for the number of generators of monomial ideals failing the WLP extending a result by Mezzetti and Miró-Roig which provides upper bounds for such ideals. In the second paper, we also study the WLP of ideals generated by forms of a certain degree invariant under an action of a cyclic group. We give a complete classication of such ideals satisfying the WLP in terms of the representation of the group generalizing a result by Mezzetti and Miró-Roig.

  • 115.
    Altafi, Nasrin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Lefschetz Properties of Monomial Ideals with Almost Linear ResolutionIn: Article in journal (Other academic)
    Abstract [en]

    We study the WLP and SLP of artinian monomial ideals in S = K[x1, . . . , xn]

    via studying their minimal free resolutions. We study the Lefschetz properties of such ideals

    where the minimal free resolution of S/I is linear for at least n − 2 steps. We give an

    affirmative answer to a conjecture of Eisenbud, Huneke and Ulrich for artinian monomial

    ideals with almost linear resolutions.

  • 116.
    Altafi, Nasrin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    The Weak Lefschetz Property of Equigenerated Monomial IdealsIn: Article in journal (Other academic)
    Abstract [en]

    We determine the sharp lower bound for the Hilbert function in degree d of a

    monomial algebra failing the WLP over a polynomial ring with n variables and generated in

    degree d. We consider artinian ideals in the polynomial ring with

    n variables generated by homogeneous polynomials of degree d invariant under an action of

    the cyclic group Z/dZ. We give a complete classification of

    such ideals in terms of the WLP depending on the action.

  • 117.
    Altafi, Nasrin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Nemati, N.
    Fakhari, S. A. S.
    Yassemi, S.
    Free resolution of powers of monomial ideals and Golod rings2017In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 120, no 1, p. 59-67Article in journal (Refereed)
    Abstract [en]

    Let S = Kdbl[x1,⋯, xn] be the polynomial ring over a field Kdbl. In this paper we present a criterion for componentwise linearity of powers of monomial ideals. In particular, we prove that if a squarefree monomial ideal I contains no variable and some power of I is componentwise linear, then I satisfies the gcd condition. For a square-free monomial ideal I which contains no variable, we show that S/I is a Golod ring provided that for some integer s ≥ 1, the ideal Is has linear quotients with respect to a monomial order.

  • 118.
    Alvehag, Karin
    et al.
    KTH, School of Electrical Engineering (EES), Electric Power Systems.
    Martin, Clyde
    Texas Tech University.
    The Feedback Control of Glucose: On the road to type II diabetes2006In: Proceedings of the 45th IEEE Conference on Decision & Control, 2006, p. 685-690Conference paper (Refereed)
    Abstract [en]

    This paper develops a mathematical model for the feedback control of glucose regulation in the healthy human being and is based on the work of Sorensen (1985). The proposed model serves as a starting point for modeling type H diabetes. Four agents - glucose and the three hormones insulin, glucagon, and incretins - are assumed to have an effect on glucose metabolism. By letting compartments represent anatomical organs, the model has a close resemblance to a real human body. Mass balance equations that account for blood flows, exchange between compartments, and metabolic sinks and sources are written, and these result in simultaneous differential equations that are solved numerically. The metabolic sinks and sources - removing or adding glucose, insulin, glucagon, and incretins - describe physiological processes in the body. These processes function as feedback control systems and have nonlinear behaviors. The results of simulations performed for three different clinical test types indicate that the model is successful in simulating intravenous glucose, oral glucose, and meals containing mainly carbohydrates.

  • 119.
    Alvfors, Oskar
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Björelind, Fredrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Optimization of Production Scheduling in the Dairy Industry2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This thesis presents a case study of mathematical production scheduling optimization applied on Arla Foods AB’s production of dairy products. The scheduling was performed as a possible remedy for problems caused by overcrowded finished goods warehouse. Based on the scheduling, conclusions were made on whether the existing two-shift production is sufficient or if an additional night shift should be introduced. In parallel, an empirical and theoretical analysis on the perceived effects of night shift work on employees was conducted.

    For the optimization, mixed integer programming was used to model the production context through a discrete time scheduling lot-sizing model developed in this thesis. The model developed and implemented on Arla Foods AB contributes to the research field through its feature of relatively low complexity enabling scheduling of extensive production systems when applied in industrial contexts where products may be categorized.

    The thesis concludes that mathematical production scheduling can solve Arla Foods AB’s production problematics and suggests reallocation of the existing shifts for the purpose of reduced costs and acceptable warehouse levels. This reallocation would incur production during inconvenient hours whereas management remedies reducing negative effects of night shift work are identified.

  • 120.
    Alvianto Priyanto, Criss
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Shift Design and Driver Scheduling Problem2018Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Scheduling problem and shift design problems are well known NP-hard problems within the optimization area. Often time, the two problems are studied individually. In this thesis however, we are looking at the combination of both problems. More specifically, the aim of this thesis is to suggest an optimal scheduling policy given that there are no predefined shifts to begin with. The duration of a shift, along with the start and end time may vary. Thus we have proposed to split the problem into two sub-problems: weekly scheduling problem and daily scheduling problem. As there are no exact solution methods that are feasible, two meta-heuristics method has been employed to solve the sub-problems: Simulated Annealing (SA) and Genetic Algorithm (GA). We have provided proofs of concepts for both methods as well as explored the scalability. This is especially important as the number of employee is expected to grow significantly throughout the year. The results obtained has shown to be promising and can be built upon for further capabilities.

  • 121. Alwen, J.
    et al.
    de Rezende, Susanna F.
    KTH.
    Nordström, Jakob
    KTH.
    Vinyals, Marc
    KTH.
    Cumulative space in black-white pebbling and resolution2017In: Leibniz International Proceedings in Informatics, LIPIcs, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing , 2017Conference paper (Refereed)
    Abstract [en]

    We study space complexity and time-space trade-offs with a focus not on peak memory usage but on overall memory consumption throughout the computation. Such a cumulative space measure was introduced for the computational model of parallel black pebbling by [Alwen and Serbinenko 2015] as a tool for obtaining results in cryptography. We consider instead the nondeterministic black-white pebble game and prove optimal cumulative space lower bounds and trade-offs, where in order to minimize pebbling time the space has to remain large during a significant fraction of the pebbling. We also initiate the study of cumulative space in proof complexity, an area where other space complexity measures have been extensively studied during the last 10-15 years. Using and extending the connection between proof complexity and pebble games in [Ben-Sasson and Nordström 2008, 2011], we obtain several strong cumulative space results for (even parallel versions of) the resolution proof system, and outline some possible future directions of study of this, in our opinion, natural and interesting space measure.

  • 122. Amerik, Ekaterina
    et al.
    Kurlberg, Pär
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Nguyen, Khoa D.
    Towsley, Adam
    Viray, Bianca
    Voloch, Jose Felipe
    Evidence for the Dynamical Brauer-Manin Criterion2016In: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 25, no 1, p. 54-65Article in journal (Refereed)
    Abstract [en]

    Let phi: X -> X be a morphism of a variety over a number field K. We consider local conditions and a "Brauer-Manin" condition, defined by Hsia and Silverman, for the orbit of a point P is an element of X(K) to be disjoint from a subvariety V subset of X, i.e., for V boolean AND O-phi (P) = empty set. We provide evidence that the dynamical Brauer-Manin condition is sufficient to explain the lack of points in the intersection V boolean AND O-phi (P); this evidence stems from a probabilistic argument as well as unconditional results in the case of etale maps.

  • 123.
    Ames, Ellery
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Beyer, F.
    Isenberg, J.
    LeFloch, P. G.
    A class of solutions to the Einstein equations with AVTD behavior in generalized wave gauges2017In: Journal of Geometry and Physics, ISSN 0393-0440, E-ISSN 1879-1662, Vol. 121, p. 42-71Article in journal (Refereed)
    Abstract [en]

    We establish the existence of smooth vacuum Gowdy solutions, which are asymptotically velocity term dominated (AVTD) and have T3-spatial topology, in an infinite dimensional family of generalized wave gauges. These results show that the AVTD property, which has so far been known to hold for solutions in areal coordinates only, is stable to perturbations of the coordinate systems. Our proof is based on an analysis of the singular initial value problem for the Einstein vacuum equations in the generalized wave gauge formalism, and provides a framework which we anticipate to be useful for more general spacetimes.

  • 124.
    Ameur, Yacin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Cwikel, Michael
    Technion Israel Inst Technol, Dept Math.
    On the K-divisibility constant for some special finite-dimensional Banach couples2009In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 360, no 1, p. 130-155Article in journal (Refereed)
    Abstract [en]

    We prove new estimates of the K-divisibility constants for some special Banach couples. In particular, we prove that the K-divisibility constant for a couple of the form (U circle plus V, U) where U and V are non-trivial Hilbert spaces equals 2/root 3. We also prove estimates for the K-divisibility constant of the two-dimensional version of the couple (L-2, L-infinity), proving in particular that this couple is not exactly K-divisible. There are also several auxiliary results, including some estimates for relative Calderon constants for finite-dimensional couples.

  • 125.
    Ameur, Yacin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Hedenmalm, Håkan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Makarov, Nikolai
    Berezin Transform in Polynomial Bergman Spaces2010In: Communications on Pure and Applied Mathematics, ISSN 0010-3640, E-ISSN 1097-0312, Vol. 63, no 12, p. 1533-1584Article in journal (Refereed)
    Abstract [en]

    Fix a smooth weight function Q in the plane, subject to a growth condition from below Let K-m,K-n denote the reproducing kernel for the Hilbert space of analytic polynomials of degree at most n - 1 of finite L-2-norm with respect to the measure e-(mQ) dA Here dA is normalized area measure, and m is a positive real scaling parameter The (polynomial) Berezin measure dB(m,n)(< z0 >) (z) = K-m,K-n(z(0).z(0))(-1) vertical bar K-m,K-n(z.z(0))vertical bar(2)e(-mQ(z)) dA(z) for the point z(0) is a probability measure that defines the (polynomial) Berezin transform B-m,B-n f(z(0)) = integral(C) f dB(m,n)(< z0 >) for continuous f is an element of L-infinity (C). We analyze the semiclassical limit of the Berezin measure (and transform) as m -> +infinity while n = m tau + o(1), where tau is fixed, positive, and real We find that the Berezin measure for z(0) converges weak-star to the unit point mass at the point z(0) provided that Delta Q(z(0)) > 0 and that z(0) is contained in the interior of a compact set f(tau). defined as the coincidence set for an obstacle problem. As a refinement, we show that the appropriate local blowup of the Berezin measure converges to the standardized Gaussian measure in the plane For points z(0) is an element of C\f(tau), the Berezin measure cannot converge to the point mass at z(0) In the model case Q(z) = vertical bar z vertical bar(2), when f(tau) is a closed disk, we find that the Berezin measure instead converges to harmonic measure at z(0) relative to C\f(tau) Our results have applications to the study of the cigenvalues of random normal matrices The auxiliary results include weighted L-2-estimates for the equation partial derivative u = f when f is a suitable test function and the solution u is restricted by a polynomial growth bound at infinity.

  • 126. Ameur, Yacin
    et al.
    Hedenmalm, Håkan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Makarov, Nikolai
    FLUCTUATIONS OF EIGENVALUES OF RANDOM NORMAL MATRICES2011In: Duke mathematical journal, ISSN 0012-7094, E-ISSN 1547-7398, Vol. 159, no 1, p. 31-81Article in journal (Refereed)
    Abstract [en]

    In this article, we consider a fairly general potential in the plane and the corresponding Boltzmann-Gibbs distribution of eigenvalues of random normal matrices. As the order of the matrices tends to infinity, the eigenvalues condensate on a certain compact subset of the plane-the "droplet." We prove that fluctuations of linear statistics of eigenvalues of random normal matrices converge on compact subsets of the interior of the droplet to a Gaussian field, and we discuss various ramifications of this result.

  • 127. Ameur, Yacin
    et al.
    Hedenmalm, Håkan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Makarov, Nikolai
    Random normal matrices and ward identities2015In: Annals of Probability, ISSN 0091-1798, E-ISSN 2168-894X, Vol. 43, no 3, p. 1157-1201Article in journal (Refereed)
    Abstract [en]

    We consider the random normal matrix ensemble associated with a potential in the plane of sufficient growth near infinity. It is known that asymptotically as the order of the random matrix increases indefinitely, the eigenvalues approach a certain equilibrium density, given in terms of Frostman's solution to the minimum energy problem of weighted logarithmic potential theory. At a finer scale, we may consider fluctuations of eigenvalues about the equilibrium. In the present paper, we give the correction to the expectation of the fluctuations, and we show that the potential field of the corrected fluctuations converge on smooth test functions to a Gaussian free field with free boundary conditions on the droplet associated with the potential.

  • 128.
    Ameur, Yacin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Kaijser, Sten
    Silvestrov, Serge
    Interpolation classes and matrix monotone functions2007In: Journal of operator theory, ISSN 0379-4024, E-ISSN 1841-7744, Vol. 57, no 2, p. 409-427Article in journal (Refereed)
    Abstract [en]

    An interpolation function of order n is a positive function -/+ on (0, infinity) such that vertical bar vertical bar -/+ (A)(1/2) T -/+ (A)-(1/2) vertical bar vertical bar <= max(vertical bar vertical bar T vertical bar vertical bar, vertical bar A(1/2)TA(-1/2) vertical bar vertical bar) for all n x ii matrices T and A such that A is positive definite. By a theorem of Donoghue, the class C-n of interpolation functions of order n coincides with the class of functions -/+ such that for each n-subset S = {lambda i}(n)(i=1)of (0,infinity) there exists a positive Pick function h on (0, co) interpolating -/+ at S. This note comprises a study of the classes C-n and their relations to matrix monotone functions of finite order. We also consider interpolation functions on general unital C*-algebras.

  • 129.
    Amini, Nima
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Equidistributions of mahonian statistics over pattern avoiding permutations2018In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 25, no 1, article id P1.7Article in journal (Refereed)
    Abstract [en]

    A Mahonian d-function is a Mahonian statistic that can be expressed as a linear combination of vincular pattern functions of length at most d. Babson and Ste- ingrímsson classified all Mahonian 3-functions up to trivial bijections and identified many of them with well-known Mahonian statistics in the literature. We prove a host of Mahonian 3-function equidistributions over permutations in Sn avoiding a single classical pattern in S3. Tools used include block decomposition, Dyck paths and generating functions.

  • 130.
    Amini, Nima
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Brändén, Petter
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Non-representable hyperbolic matroids2018In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 334, p. 417-449Article in journal (Refereed)
    Abstract [en]

    The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. Hyperbolic polynomials give rise to a class of (hyperbolic) matroids which properly contains the class of matroids representable over the complex numbers. This connection was used by the second author to construct counterexamples to algebraic (stronger) versions of the generalized Lax conjecture by considering a non-representable hyperbolic matroid. The Vamos matroid and a generalization of it are, prior to this work, the only known instances of non-representable hyperbolic matroids. We prove that the Non-Pappus and Non-Desargues matroids are non-representable hyperbolic matroids by exploiting a connection between Euclidean Jordan algebras and projective geometries. We further identify a large class of hyperbolic matroids which contains the Vamos matroid and the generalized Vamos matroids recently studied by Burton, Vinzant and Youm. This proves a conjecture of Burton et al. We also prove that many of the matroids considered here are non representable. The proof of hyperbolicity for the matroids in the class depends on proving nonnegativity of certain symmetric polynomials. In particular we generalize and strengthen several inequalities in the literature, such as the Laguerre Turan inequality and an inequality due to Jensen. Finally we explore consequences to algebraic versions of the generalized Lax conjecture.

  • 131. Ammann, B.
    et al.
    Dahl, Mattias
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Humbert, E.
    The conformal Yamabe constant of product manifolds2013In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 141, no 1, p. 295-307Article in journal (Refereed)
    Abstract [en]

    Let (V, g) and (W, h) be compact Riemannian manifolds of dimension at least 3. We derive a lower bound for the conformal Yamabe constant of the product manifold (V × W, g + h) in terms of the conformal Yamabe constants of (V, g) and (W, h).

  • 132. Ammann, Bernd
    et al.
    Dahl, Mattias
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Hermann, Andreas
    Humbert, Emmanuel
    Mass endomorphism, surgery and perturbations2014In: Annales de l'Institut Fourier, ISSN 0373-0956, E-ISSN 1777-5310, Vol. 64, no 2, p. 467-487Article in journal (Refereed)
    Abstract [en]

    We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.

  • 133. Ammann, Bernd
    et al.
    Dahl, Mattias
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Humbert, Emmanuel
    Harmonic spinors and local deformations of the metric2011In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 18, no 5, p. 927-936Article in journal (Refereed)
    Abstract [en]

    Let (M, g) be a compact Riemannian spin manifold. The Atiyah-Singer index theorem yields a lower bound for the dimension of the kernel of the Dirac operator. We prove that this bound can be attained by changing the Riemannian metric g on an arbitrarily small open set.

  • 134. Ammann, Bernd
    et al.
    Dahl, Mattias
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Humbert, Emmanuel
    Low-dimensional surgery and the Yamabe invariant2015In: Journal of the Mathematical Society of Japan, ISSN 0025-5645, E-ISSN 1881-1167, Vol. 67, no 1, p. 159-182Article in journal (Refereed)
    Abstract [en]

    Assume that M is a compact n-dimensional manifold and that N is obtained by surgery along a k-dimensional sphere, k <= n - 3. The smooth Yamabe invariants sigma(M) and sigma(N) satisfy sigma(N) >= min(sigma(M), Lambda) for a constant Lambda > 0 depending only on n and k. We derive explicit positive lower bounds for A in dimensions where previous methods failed, namely for (n, k) is an element of {(4, 1), (5, 1), (5, 2), (6, 3), (9, 1), (10, 1)}. With methods from surgery theory and bordism theory several gap phenomena for smooth Yamabe invariants can be deduced.

  • 135. Ammann, Bernd
    et al.
    Dahl, Mattias
    Humbert, Emmanuel
    Smooth yamabe invariant and surgery2013In: Journal of differential geometry, ISSN 0022-040X, E-ISSN 1945-743X, Vol. 94, no 1, p. 1-58Article in journal (Refereed)
    Abstract [en]

    We prove a surgery formula for the smooth Yamabe invariant sigma(M) of a compact manifold M. Assume that N is obtained from M by surgery of codimension at least 3. We prove the existence of a positive constant Lambda(n), depending only on the dimension n of M, such that sigma(N) >= min{sigma(M), Lambda(n)}.

  • 136. Ammann, Bernd
    et al.
    Dahl, Mattias
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Humbert, Emmanuel
    Square-integrability of solutions of the Yamabe equation2013In: Communications in analysis and geometry, ISSN 1019-8385, E-ISSN 1944-9992, Vol. 21, no 5, p. 891-916Article in journal (Refereed)
    Abstract [en]

    We show that solutions of the Yamabe equation on certain n-dimensional non-compact Riemannian manifolds, which are bounded and L-p for p = 2n/(n -2) are also L-2. This L-p-L-2 implication provides explicit constants in the surgery-monotonicity formula for the smooth Yamabe invariant in our paper [4]. As an application we see that the smooth Yamabe invariant of any two-connected compact seven-dimensional manifold is at least 74.5. Similar conclusions follow in dimension 8 and in dimensions >= 11.

  • 137. Ammann, Bernd
    et al.
    Dahl, Mattias
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Humbert, Emmanuel
    Surgery and harmonic spinors2009In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 220, no 2, p. 523-539Article in journal (Refereed)
    Abstract [en]

    Let M he a compact spin manifold with a chosen spin structure. The Atiyah-Singer index theorem implies that for any Riemannian metric on M the dimension of the kernel of the Dirac operator is bounded from below by a topological quantity depending only on M and the spin structure. We show that for generic metrics on M this bound is attained.

  • 138. Ammann, Bernd
    et al.
    Dahl, Mattias
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Humbert, Emmanuel
    Surgery and the Spinorial tau-Invariant2009In: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 34, no 10, p. 1147-1179Article in journal (Refereed)
    Abstract [en]

    We associate to a compact spin manifold M a real-valued invariant (M) by taking the supremum over all conformal classes of the infimum inside each conformal class of the first positive Dirac eigenvalue, when the metrics are normalized to unit volume. This invariant is a spinorial analogue of Schoen's sigma-constant, also known as the smooth Yamabe invariant. We prove that if N is obtained from M by surgery of codimension at least 2 then (N) epsilon min{(M), n}, where n is a positive constant depending only on n=dim M. Various topological conclusions can be drawn, in particular that is a spin-bordism invariant below n. Also, below n the values of cannot accumulate from above when varied over all manifolds of dimension n.

  • 139.
    Ammar, Ofir
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    A thesis submitted in fulfilment of the requirements for the degree of Masters of Mathematics2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    An open problem introduced by J. Haglund was to find a bijective proof over Dyck paths that would interchange two of its statistics. This problem was known to be The Symmetry Problem of the q,t-Catalan polynomial and was proven by other means to be true. This project is an attempt to find a bijection, where we provide the bijection's behaviour under certain constrains. Then, we introduce an attempt to translate the problem from Dyck paths to other combinatorial structures. Finally we try to solve a related conjecture, called The Symmetry Problem of parking functions, which generalizes the previous problem. Some results we obtained from The Symmetry Problem of parking functions helped us characterize part of a bijective proof for Dyck paths.

  • 140.
    Amsköld, Daniel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    A comparison between different volatility models2011Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
  • 141.
    Amundsson, Karl
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Approximate Bayesian Learning of Partition Directed Acyclic Graphs2016Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Partition directed acyclic graphs (PDAGs) is a model whereby the conditional probability tables (CPTs) are partitioned into parts with equal probability. In this way, the number of parameters that need to be learned can be significantly reduced so that some problems become more computationally feasible. PDAGs have been shown to be connected to labeled DAGs (LDAGs) and the connection is summarized here. Furthermore, a clustering algorithm is compared to an exact algorithm for determining a PDAG. To evaluate the algorithm, we use it on simulated data where the expected result is known.

  • 142.
    Amundsson, Karl
    KTH, School of Engineering Sciences (SCI).
    Morphisms of Fusion Systems2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    A fusion system on a finite group G with a Sylow p-subgroup P is a category on P with all subgroups of P as objects and group homomorphisms induced by conjugation in G as morphisms and was first introduced by L. Puig around 1990 in order to aid his research in finite group theory. The idea turned out to be fruitful and today, the theory of fusion systems is an active field in mathematics, with applications to topology, representation theory and finite group theory.

    In this paper, we will, among other things, see how fusion systems aid in solving problems in finite group theory. We begin with an introduction to the theory with basic examples and then proceed to prove two famous theorems named after Burnside and Frobenius. However, to finish the proof of Frobenius’ theorem, we will require the focal subgroup theorem, whose proof requires transfer theory and is thus discussed. Afterwards, we introduce abstract and saturated fusion systems, in which one disregard the underlying group, and later prove that every fusion system on a finite group is saturated. We end with a discussion of morphisms of fusion systems, utilizing the concept previously developed, and generalize the isomorphism theorems to saturated fusion systems.

    The presentation is well adapted for undergraduate students with limited knowledge of group and category theory and no previous knowledge of fusion systems is assumed.

  • 143.
    Anderl, Daniela
    KTH, School of Computer Science and Communication (CSC).
    Modeling of a Cooling Airflow in an Electric Motor.2011Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    An electric motor converts electrical to mechanical energy and provides the rotational torque which is converted into linear motion. In some applications the duty is cyclic and the motor is used for both providing driving and breaking torque. In many applications today, the power to weight requirements are continuously increasing which means that the cooling is crucial. One of the major design elements in the cooling system of an electric motor is the fan. Unfortunately the current fan exceeds the noise constraints. The thesis analyses the fan in terms of noise production and performance, and proposes an improved fan design. The computation of the airflow is done with the software COMSOL. In the beginning different design guidelines and noise sources of a fan in general are summarized. Subsequently the concrete simulation procedure in COMSOL is described. After these basic issues are discussed, the different noise sources, namely the broad-band and the tonal noise, are investigated for the current fan and the improved fan design. The analysis of different design-space parameters is also done in terms of performance of the fan, i.e. the actual transported airflow together with the produced pressure difference. In the end, the results of these studies are summarized and the most improved fan design is the outcome of this.

  • 144.
    Andersson, Alexandra
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Smart Beta Investering Baserad på Makroekonomiska Indikatorer2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis examines the possibility to find a relationship between the Nasdaq Nordea Smart Beta Indices and a series of macroeconomic indicators. This relationship will be used as a signal-value and implemented in a portfolio consisting of all six smart beta indices. To investigate the impact of the signal-value on the portfolio performance, three portfolio strategies are examined with the equally weighted portfolio as a benchmark. The portfolio weights will be re-evaluated monthly and the portfolios examined are the mean-variance portfolio, the mean-variance portfolio based on the signal-value and the equally weighted portfolio based on the signal-value.

    In order to forecast the performance of the portfolio, a multivariate GARCH model with time-varying correlations is fitted to the data and three different error-distributions are considered. The performances of the portfolios are studied both in- and out-of-sample and the analysis is based on the Sharpe ratio.

    The results indicate that a mean-variance portfolio based on the relationship with the macroeconomic indicators outperforms the other portfolios for the in-sample period, with respect to the Sharpe ratio. In the out-of-sample period however, none of the portfolio strategies has Sharpe ratios that are statistically different from that of an equally weighted portfolio.

  • 145.
    Andersson, Daniel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    A mixed relaxed singular maximum principle for linear SDEs with random coefficientsArticle in journal (Refereed)
    Abstract [en]

    We study singular stochastic control of a two dimensional stochastic differential equation, where the first component is linear with random and unbounded coefficients. We derive existence of an optimal relaxed control and necessary conditions for optimality in the form of a mixed relaxed-singular maximum principle in a global form. A motivating example is given in the form of an optimal investment and consumption problem with transaction costs, where we consider a portfolio with a continuum of bonds and where the portfolio weights are modeled as measure-valued processes on the set of times to maturity.

  • 146.
    Andersson, Daniel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Contributions to the Stochastic Maximum Principle2009Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis consists of four papers treating the maximum principle for stochastic control problems.

    In the first paper we study the optimal control of a class of stochastic differential equations (SDEs) of mean-field type, where the coefficients are allowed to depend on the law of the process. Moreover, the cost functional of the control problem may also depend on the law of the process. Necessary and sufficient conditions for optimality are derived in the form of a maximum principle, which is also applied to solve the mean-variance portfolio problem.

    In the second paper, we study the problem of controlling a linear SDE where the coefficients are random and not necessarily bounded. We consider relaxed control processes, i.e. the control is defined as a process taking values in the space of probability measures on the control set. The main motivation is a bond portfolio optimization problem. The relaxed control processes are then interpreted as the portfolio weights corresponding to different maturity times of the bonds. We establish existence of an optimal control and necessary conditons for optimality in the form of a maximum principle, extended to include the family of relaxed controls.

    The third paper generalizes the second one by adding a singular control process to the SDE. That is, the control is singular with respect to the Lebesgue measure and its influence on the state is thus not continuous in time. In terms of the portfolio problem, this allows us to consider two investment possibilities - bonds (with a continuum of maturities) and stocks - and incur transaction costs between the two accounts.

    In the fourth paper we consider a general singular control problem. The absolutely continuous part of the control is relaxed in the classical way, i.e. the generator of the corresponding martingale problem is integrated with respect to a probability measure, guaranteeing the existence of an optimal control. This is shown to correspond to an SDE driven by a continuous orthogonal martingale measure. A maximum principle which describes necessary conditions for optimal relaxed singular control is derived.

  • 147.
    Andersson, Daniel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Necessary Optimality Conditions for Two Stochastic Control Problems2008Licentiate thesis, comprehensive summary (Other scientific)
    Abstract [en]

    This thesis consists of two papers concerning necessary conditions in stochastic control problems. In the first paper, we study the problem of controlling a linear stochastic differential equation (SDE) where the coefficients are random and not necessarily bounded. We consider relaxed control processes, i.e. the control is defined as a process taking values in the space of probability measures on the control set. The main motivation is a bond portfolio optimization problem. The relaxed control processes are then interpreted as the portfolio weights corresponding to different maturity times of the bonds. We establish existence of an optimal control and necessary conditions for optimality in the form of a maximum principle, extended to include the family of relaxed controls.

    In the second paper we consider the so-called singular control problem where the control consists of two components, one absolutely continuous and one singular. The absolutely continuous part of the control is allowed to enter both the drift and diffusion coefficient. The absolutely continuous part is relaxed in the classical way, i.e. the generator of the corresponding martingale problem is integrated with respect to a probability measure, guaranteeing the existence of an optimal control. This is shown to correspond to an SDE driven by a continuous orthogonal martingale measure. A maximum principle which describes necessary conditions for optimal relaxed singular control is derived.

  • 148.
    Andersson, Daniel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    The relaxed general maximum principle for singular optimal control of diffusions2009In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, ISSN 01676911, Vol. 58, no 1, p. 76-82Article in journal (Refereed)
    Abstract [en]

    In this paper we study optimality in stochastic control problems where the state process is a stochastic differential equation (SDE) and the control variable has two components, the first being absolutely continuous and the second singular. A control is defined as a solution to the corresponding martingale problem. To obtain existence of an optimal control Haussmann and Suo [U.G. Haussmann, W. Suo, Singular optimal stochastic controls I: Existence, SIAM J. Control Optim. 33 (3) (1995) 916-936] relaxed the martingale problem by extending the absolutely continuous control to the space of probability measures on the control set. Bahlali et al. [S. Bahlali, B. Djehiche, B. Mezerdi, The relaxed stochastic maximum principle in singular optimal control of diffusions, SIAM J. Control Optim. 46 (2) (2007) 427-444] established a maximum principle for relaxed singular control problems with uncontrolled diffusion coefficient. The main goal of this paper is to extend their results to the case where the control enters the diffusion coefficient. The proof is based on necessary conditions for near optimality of a sequence of ordinary controls which approximate the optimal relaxed control. The necessary conditions for near optimality are obtained by Ekeland's variational principle and the general maximum principle for (strict) singular control problems obtained in Bahlali and Mezerdi [S. Bahlali, B. Mezerdi, A general stochastic maximum principle for singular control problems, Electron J. Probab. 10 (2005) 988-1004. Paper no 30]. © 2008 Elsevier B.V. All rights reserved.

  • 149.
    Andersson, Daniel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    The relaxed stochastic maximum principle in singular optimal control of diffusions with controlled diffusion coefficientManuscript (Other academic)
  • 150.
    Andersson, Daniel
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Djehiche, Boualem
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    A maximum principle for relaxed stochastic control of linear SDEs with application to bond portfolio optimization2010In: Mathematical Methods of Operations Research, ISSN 1432-2994, E-ISSN 1432-5217, Vol. 72, no 2, p. 273-310Article in journal (Refereed)
    Abstract [en]

    We study relaxed stochastic control problems where the state equation is a one dimensional linear stochastic differential equation with random and unbounded coefficients. The two main results are existence of an optimal relaxed control and necessary conditions for optimality in the form of a relaxed maximum principle. The main motivation is an optimal bond portfolio problem in a market where there exists a continuum of bonds and the portfolio weights are modeled as measure-valued processes on the set of times to maturity.

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