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• 1.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
In times of regional geopolitical turmoil – Why do some equity funds performbetter than others?2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

In times of regional geopolitical turmoil – why do some investment portfolios, equity funds, perform better than others? Is it simply luck, the effects of systematic risk or do factors such as investment styles and managerial skills play a significant part in the performance of a fund?

As financial markets often reflect the macro environment, much of the previous year’s fluctuations of Eastern European stocks can be seen to derive from a number of geopolitical events; from the 2013 summer clashes between the Turkish police and opposing parties to the current issue concerning Russia and Ukraine. Needless to say, these events have affected return on equity in their regions and created a distressed environment for investors and equity fund managers investing in Eastern Europe.

This thesis aims to explore how the aforementioned macroeconomic events impact the market and thus the portfolios of asset managers. The thesis also intends to provide aspects of eventual investment strategies that are more preferable than others under such circumstances, in order to mitigate the subsequent risks.

• 2.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
ESG-investerande och portföljresultat: En studie av ESG-investerande utifrån metoden bäst-i-klassen2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

As a result of a more globalized and industrial world, sustainability issues in terms of the environment and society has become an everyday heading in the financial world. The fact that companies should work actively towards sustainability and accountability is today a necessity rather than a choice. The purpose of this study is to research responsible investment (RI) and portfolio performance. To examine this relationship the study focuses on ESG where its dimensions will be included jointly through optimization, discussion and conclusion. The report outlines how ESG can be integrated into the investment process, but the weight of the study addresses the discussion of a portfolio's performance at the inclusion of ESG. Methods used are Modern Portfolio Theory (MPT) combined with the implementation of ESG according to "best-in-class". The results of the study lead towards the conclusion that ESG in addition to its positive effects, provided an accurate assessment, on sustainability also is financially arguable for investors.

• 3.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Analys av reporäntans påverkan på prissättningen av bostäder: Slår reporänteförändringar lika mycket på bostäder av olika storlek?2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

The aim of this study is to investigate whether changes of the repo rate has diverse effects on apartments of different sizes, targeting specific areas in Stockholm. A conclusion, that the effect of the repo rate differs for apartments of different sizes, was made based on regression analysis and hypothesis testing. The housing market is characterized by vast shifts and the repo rate has reached a historical low-point of -0.25 per cent. It is reflected upon how the central bank’s steering interest rate actually impacts the prices on the housing market and whether it has distinct effects on apartments of different sizes. Apartments sold between years 2005-2015 have been analyzed where the gravity of the repo rate has been taken into consideration and if its significance varies amongst apartments of different sizes. Important parameters concerning apartment prices have been utilized in the constructed model.

• 4.
Yerevan State University.
Nonlinear approximation by renormalized trigonometric system2012In: Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), ISSN 1068-3623, Vol. 47, no 2, p. 86-96Article in journal (Refereed)

We study the convergence of greedy algorithmwith regard to renormalized trigonometric system. Necessary and sufficient conditions are found for system’s normalization to guarantee almost everywhere convergence, and convergence in Lp(T) for 1 < p < ∞ of the greedy algorithm, where T is the unit torus. Also the non existence is proved for normalization which guarantees convergence almost everywhere for functions from L1(T), or uniform convergence for continuous functions.

• 5.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). Yerevan State University, Armenia.
On greedy algorithm by renormed Franklin system2010In: East Journal on Approximations, ISSN 1310-6236, Vol. 16, no 3, p. 273-296Article in journal (Refereed)

We characterize the all weighted greedy algorithms with respect to Franklin system which converge uniformly for continuous functions and almost everywhere for integrable functions. In case, when the algorithm fails to satisfy our classification criteria, we construct a continuous function for which the corresponding approximation diverges unboundedly almost everywhere. Some applications to wavelet systems are also discussed.

• 6.
Yerevan State University.
On the greedy algorithm by the Haar system2010In: Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), ISSN 1068-3623, Vol. 45, no 3, p. 151-161Article in journal (Refereed)

The paper investigates the uniform and almost everywhere convergence of the greedy algorithm by the Haar system. Necessary and sufficient conditions for norming the functions of Haar system are obtained, which guarantee the uniformconvergence for functions from C[0, 1] and almost everywhere convergence for functions from L1[0, 1].

• 7.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). The University of Edinburgh, UK.
Regularity of boundary data in periodic homogenization of elliptic systems in layered media2017In: Manuscripta mathematica, ISSN 0025-2611, E-ISSN 1432-1785, Vol. 154, no 1-2, p. 225-256Article in journal (Refereed)

In this note we study periodic homogenization of Dirichlet problem for divergence type elliptic systems when both the coefficients and the boundary data are oscillating. One of the key difficulties here is the determination of the fixed boundary data corresponding to the limiting (homogenized) problem. This issue has been addressed in recent papers by Gérard-Varet and Masmoudi (Acta Math. 209:133–178, 2012), and by Prange (SIAM J. Math. Anal. 45(1):345–387, 2012), however, not much is known about the regularity of this fixed data. The main objective of this note is to initiate a study of this problem, and to prove several regularity results in this connection.

• 8.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
The University of Edinburgh.
K-surfaces with free boundaries2017Article in journal (Refereed)
• 9.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Discrete balayage and boundary sandpile2016In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538Article in journal (Refereed)
• 10.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Perturbed divisible sandpiles and quadrature surfaces2017Article in journal (Refereed)
• 11.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). The University of Edinburgh.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
L2-estimates for singular oscillatory integral operators2016In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 441, no 2, p. 529-548Article in journal (Refereed)

In this note we study singular oscillatory integrals with linear phase function over hypersurfaces which may oscillate, and prove estimates of L2L2 type for the operator, as well as for the corresponding maximal function. If the hypersurface is flat, we consider a particular class of a nonlinear phase functions, and apply our analysis to the eigenvalue problem associated with the Helmholtz equation in R3.

• 12.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
Optimering av antal flygplanssäten: Modellering med avseende på yta, intäkt och efterfrågan 2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

When managing the number of seats in a plane it is important to take into account the passenger intensity, i.e. how tightly the seats are located. The critical variable for these decisions is the distance between a point on one seat and the same point on the next seat. Critical variables that have small values , i.e. short distance, means more rows of seats and thus higher profits. Any unused space is an expensive waste due to the fact that the difference between profit and loss for a given flight can be as little as less than a cost of a seat.

The purpose of this thesis is to develop a mathematical model to find the optimal seat allocation between classes in an airplane. The modeling shall be performed so that the revenues for the airlines and usage of the surface of the cabin are maximized and yet meet demand. This thesis also aims to investigate which different market strategies of airlines there are and how these affect the seat allocation.

The report shows that the revenue and demand are not the only factors that affect the optimal number of seats for a class, but that there are also external factors that may play a role. The model's ranking in reality is difficult to assess because of the lack of realistic and reliable data that can be used for a basis for decisions

• 13.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Valuing Patents with Linear Regression: Identifying value indicators and using a linear regression model to value  patents2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

This thesis consist of two parts. The first part of the thesis will conduct a multiple regression on a data-set obtained from the Ocean Tomo’s auction results between 2006 to 2008 with the purpose to identify key value indicators and investigate to what extent it is possible to predict the value of a patent. The final regression model consist of the following covariates Average number of citings per year, share of active family members, age of the patent, average invested USD per year, and nine CPC’s as dummy variables. The second part of the thesis will investigate why it is difficult to value a patent and the different factors and changes that have contributed to a growing importance of patent valuation by applying theories from knowledge-based economy and industrial change. This is done by conducting a literature review and interviews.

The results of this thesis states that it is only possible to construct a model that has an explanation degree of 50.21%. The complexity of a patents value derives from uncertainties about future context of the patent and non-quantifiable parameters of the patent. Furthermore we find evidence of a shift from tangible assets to intangible assets in industrial nations which motivates the growing importance of patent valuation.

• 14.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
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

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.

• 15.
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

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.

• 16.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
On Invertibility of the Radon Transform and Compressive Sensing2014Doctoral thesis, comprehensive summary (Other academic)

This thesis contains three articles. The first two concern inversion andlocal injectivity of the weighted Radon transform in the plane. The thirdpaper concerns two of the key results from compressive sensing.In Paper A we prove an identity involving three singular double integrals.This is then used to prove an inversion formula for the weighted Radon transform,allowing all weight functions that have been considered previously.Paper B is devoted to stability estimates of the standard and weightedlocal Radon transform. The estimates will hold for functions that satisfy an apriori bound. When weights are involved they must solve a certain differentialequation and fulfill some regularity assumptions.In Paper C we present some new constant bounds. Firstly we presenta version of the theorem of uniform recovery of random sampling matrices,where explicit constants have not been presented before. Secondly we improvethe condition when the so-called restricted isometry property implies the nullspace property.

• 17.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Stockholm University.
Stability estimates with a priori bound for the inverse local Radon transformManuscript (preprint) (Other academic)

We consider the inverse problem for the 2-dimensional weighted local Radon transform $R_{m}[f]$, where $f$ is supported in $y\geq x^2$ and $R_{m}[f](\xi,\eta)=\int f(x,\xi x+\eta)m(x,\xi,\eta)dx$ is defined near $(\xi,\eta)=(0,0)$. For weight functions satisfying a certain differential equation we give weak estimates of$f$ in terms of $R_{m}[f]$ for functions $f$ that satisfies an a priori bound.

• 18.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
A study of the most important volume drivers for sparkling wine in Sweden2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

This paper examines the factors that affect volume of sparkling wine sold at licensed Swedish liquor stores. Regression analysis is used to model the relationship between the identified parameters believed to have an impact on the volume sold.

Social sustainability is also covered, and will be examined in the context of a deregulated alcohol market in the future. A 5C analysis and an analysis based on both WACOSS Social Sustainability framework and Social Life’s framework have been conducted.

Results from the regression analysis show that the parameters which affected the volume sold fell into three categories: Country, what kind of grape, and price. Most parameters affected the volume sold in a positive way; except for wines from New Zealand and higher priced wine which reduce the volume sold.

This thesis arrives at the conclusion that a regulated alcohol market is favorable in Sweden since the aim is to keep the alcohol consumption low and the overall public health high.

• 19.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Prediction of French day-ahead electricity prices: Comparison between a deterministic and a stochastic approach2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

This thesis deals with the new flow-based computation method used in the Central Western Europe Area. This is done on the financial side. The main aim is to produce some robust methods for predicting. Two approaches are used: the first one is based on a deterministic and algorithmic method involving the study of the interaction between the fundamentals and the prices. The other one is a more statistical approach based on a time series modeling of the French flow-based prices. Both approaches have advantages and disadvantages which will be discussed in the following. The work is mainly based on global simulated data provided by CASC in their implementation phase of the flow-base in Western Europe.

• 20. Arakelyan, A.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
Multi-Phase Quadrature Domains and a Related Minimization Problem2016In: Potential Analysis, ISSN 0926-2601, E-ISSN 1572-929X, p. 1-21Article in journal (Refereed)

In this paper we introduce the multi-phase version of the so-called Quadrature Domains (QD), which refers to a generalized type of mean value property for harmonic functions. The well-established and developed theory of one-phase QD was recently generalized to a two-phase version, by one of the current authors (in collaboration). Here we introduce the concept of the multi-phase version of the problem, and prove existence as well as several properties of such solutions. In particular, we discuss possibilities of multi-junction points.

• 21.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
Optimal löptidsallokering av bostadslån2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

This Bachelor’s thesis introduces a dynamic method for allocation of adjustable-rate mortgages which can be used to reduce a growing social problem. The Swedish household’s debt has steadily increased and the primary cause is mortgages loans, used to fund the purchase of a real property. Because of a period of rising home prices, Swedes are mortgaged more than ever [1]. If interest rates go up there is an increased risk of not managing the interest charge which is the greatest expense for many households.

However, there is an absence in the debate of the importance of efficient and safe mortgages. By means of the introduced dynamic method, this thesis optimizes the allocation of adjustable-rate mortgages, using both historical and future cases. In the forecasting case, expected interest charge and risk are being minimized. More specifically, the method consider three levels of risk which all values expected interest charge and risk differently. Further, the goal is to apply the dynamic method for decision support in reality and also commercialize as a business idea.

Modeling mortgage as a network flow is essential for the dynamic method. This way enables analysis of mortgages during a period of time which is necessary for determining an optimal allocation of adjustable-rate mortgages. The result from the historical case shows that shorter adjustment periods have been more favorable. Though, to an extent lower than expected – only during seven out of the last seventeen years. In addition, the results from the forecasting case indicate that it is advantageous to choose longer adjustment periods. Finally introduces a business model for the startup company, Looptime AB, of which business idea is toadminister mortgages for households, residents’ associations and non-financial companies.

• 22.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
The SVI implied volatility model and its calibration2014Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

The SVI implied volatility model is a parametric model for stochastic implied volatility.The SVI is interesting because of the possibility to state explicit conditions on its parameters so that the model does not generate prices where static arbitrage opportunities can occur. Calibration of the SVI model to real market data requires non-linear optimization algorithms and can be quite time consuming. In recent years, methods to calibrate the SVI model that use its inherent structure to reduce the dimensions of the optimization problem have been invented in order to speed up the calibration. The ?first aim of this thesis is to justify the use of the model and the no static arbitrage conditions from a theoretic point of view. Important theorems by Kellerer and Lee and their proofs are discussed in detail and the conditions are carefully derived. The second aim is to implement the model so that it can be calibrated to real market implied volatility data. A calibration method is presented and the outcome of two numerical experiments validate it. The performance of the calibration method introduced in this thesis is measured in how big a fraction of the total market volume the method manages to ?t within the market spread. Tests show that the model manages to ?t most of the market volume inside the spread, even for options with short time to maturity. Further tests show that the model is capable to recalibrate an SVI parameter set that allows for static arbitrage opportunities into an SVI parameter set that does not.

• 23.
KTH, School of Computer Science and Communication (CSC), Computational Science and Technology (CST). Aalto Univ ;Chinese Acad Sci.
Global Estimates of Errors in Quantum Computation by the Feynman-Vernon Formalism2018In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 171, no 5, p. 745-767Article in journal (Refereed)

The operation of a quantum computer is considered as a general quantum operation on a mixed state on many qubits followed by a measurement. The general quantum operation is further represented as a Feynman-Vernon double path integral over the histories of the qubits and of an environment, and afterward tracing out the environment. The qubit histories are taken to be paths on the two-sphere as in Klauder's coherent-state path integral of spin, and the environment is assumed to consist of harmonic oscillators initially in thermal equilibrium, and linearly coupled to to qubit operators . The environment can then be integrated out to give a Feynman-Vernon influence action coupling the forward and backward histories of the qubits. This representation allows to derive in a simple way estimates that the total error of operation of a quantum computer without error correction scales linearly with the number of qubits and the time of operation. It also allows to discuss Kitaev's toric code interacting with an environment in the same manner.

• 24.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Analys av variabler som påverkar lönsamheten i gymbranschen med multipel linjär regression2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

This thesis combines mathematical statistics with industrial economics and management to examine the profitability of the fitness industry in Sweden. The study was conducted with a dozen fitness businesses and the data mainly consisted of the companies’ annual reports from 2009 to 2014. The operating margin is the measure for profitability used in the calculations. A survey was conducted with multiple linear regressions to identify explanatory variables that affect the profitability and the extent of influence by these variables. The results of the regression analysis are discussed from economic aspects. This thesis contributes with strategic conclusions to the development of a business model for new and existing fitness businesses that aim to maximize profitability. The thesis can also be used as a tool in strategic development and give insight to how companies should approach the market. It includes an analysis of the competitive forces and external factors that may affect companies in the industry. Risk factors and growth opportunities are taken into account in the discussion about how companies can finance their operations. The regression analysis concludes that it is primarily the factors that affect the companies’ revenues and costs that have a significant impact on profitability. However, the results of the thesis also indicate that qualitative factors have a major impact on profitability.

• 25.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
Optimering av ett kösystem på IKEA Kungens Kurva2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

Detta arbete har undersökt hur många betjäningsstationer avdelningen Byten och Återköp på IKEA Kungens Kurva behöver för att nå en förväntad kötid inom nio minuter.  Arbetet är uppdelat i en kvantitativ del samt en kvalitativ del.

Den kvantitativa delen av arbetet besvarade den matematiska frågeställningen där kön var modellerad enligt ett M|M|c-­‐system med Poissonfördelade ankomstintensiteter samt exponentialfördelade betjäningsintensiteter.  Resultatet var baserat på data från januari 2015.  I första hand reglerades antal betjäningsstationer för att nå en förväntad kötid under nio minuter.  I andra hand reglerades betjäningsintensiteten, om kötiden ännu inte uppnåtts.  Den kvalitativa delen av arbetet baserades på ett teoretiskt ramverk gällande Customer Relationship Management samt intervjuer med Avdelningschefen och Kundrelationschefen på IKEA Kungens Kurva.  Arbetets slutsats baserades på resultat från både den kvantitativa och den kvalitativa delen av arbetet.

Det matematiska resultatet presenterar antalet öppna betjäningsstationer som krävdes timme för timme under vardagar respektive helger för att nå en förväntad kötid under nio minuter.  Slutsatsen är att i de fall där den förväntade kötiden var strax över nio minuter kommer detta inte påverka kundrelationen, så länge en god betjäning ges, medan det matematiska resultatet bör tillämpas om den förväntade kötiden är långt över nio minuter.

• 26.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Dependence Modelling and Risk Analysis in a Joint Credit-Equity Framework2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

This thesis is set in the intersection between separate types of financial markets, with emphasis on joint risk modelling. Relying on empirical findings pointing toward the ex- istence of dependence across equity and corporate debt markets, a simulation framework intended to capture this property is developed. A few different types of models form building blocks of the framework, including stochastic processes describing the evolution of equity and credit risk factors in continuous time, as well as a credit rating based model, providing a mechanism for imposing dependent credit migrations and defaults for firms participating in the market. A flexible modelling framework results, proving capable of generating dependence of varying strength and shape, across as well as within studied markets. Particular focus is given to the way markets interact in the tails of the distributions. By means of simulation, it is highlighted that dependence as produced by the model tends to spread asymmetrically with simultaneously extreme outcomes occurring more frequently in lower than in upper tails. Attempts to fit the model to observed market data featuring historical stock index and corporate bond index values are promising as both marginal distributions and dependence connecting the investigated asset types appear largely replicable, although we conclude further validation remains.

• 27.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
Modelling and Control of a Fixed-wing UAV for Landings on Mobile Landing Platforms2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

Landing on mobile landing platforms could eliminate the need for landing gear. This would particularly benefit high altitude solar UAV, which typically have a very limited payload. Such landings would however require a precise and decoupled control of the UAV’s altitude and speed. In this thesis, a small UAV is modelled, and a flight control system suitable for such landings is developed.

The aerodynamic properties of the UAV were estimated using the vortex lattice method. Propeller performance data was obtained from the manufacturer and used in the propulsion model. The complete UAV model was validated using data from test flights. A comparison of period and damping of the dynamic modes showed a good agreement (<10% error) with the flight data, except for the phugoid damping, which was too low in the model.

The model was used to design two flight control systems, one consisting of three SISO loops for altitude, airspeed and course; and another using a TECS-based controller for airspeed and altitude. Extensive testing in simulation and flight revealed a superior performance of the TECS-based controller, especially in the ability to decouple altitude and airspeed responses.

• 28.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Studie av korrelation mellan valutapar relaterade till Skandinavien2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

Is there a correlation between exchange rates for currency pairs related to Scandinavia? How can this information be used in foreign exchange trading?

This Bachelor’s thesis in Mathematical Statistics and Industrial Management aims to investigate the correlation between prices for currency pairs on the Scandinavian market. The problem formulation for the mathematical part has been designed in cooperation with Pär Hellström, a Senior Quant Trader at the electronic foreign exchange trading department at SEB. Pärs main responsibilities is to manage and develop models that are used for algorithmic currency trading. The result of the correlation study is supposed to contribute additional knowledge about the correlation on the Scandinavian currency market.

The Bachelor’s thesis is divided into several parts. The purpose of the first part is to give a background about currency trading, electronic foreign exchange trading and algorithmic trading.

In the subsequent part in Mathematical Statistics the correlation study is conducted. The study of correlation is made for a long time interval and for a number of shorter time intervals over the same time period in order to determine if there are periods when the correlation of the studied currency pairs change drastically. Data for the currency pairs are modified and a simple linear regression is performed for two currency pairs at a time. Based on the regressions, correlation coefficients and their significance is calculated. The correlation study shows that for the longer time interval there is a significant and strong or very strong correlation or anticorrelation between several of the currency pairs related to Scandinavia. Furthermore, the correlation study shows that the correlation is dependent on the studied time interval and that all combinations of currency pairs exhibit correlation changes over time. The changes in correlation between two currency pairs are primarily due

to a large price change for one or both of the currency pairs.

• 29.
Weierstrass Institute for Applied Analysis and Stochastics.
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30). KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30). Dept. of Mathematical Sciences, University of Delaware. KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30). KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30). Division of Mathematics, King Abdullah University of Science and Technology.
How accurate is molecular dynamics?2012Report (Other academic)

Born-Oppenheimer dynamics is shown to provide an accurate approximation of time-independent Schrödinger observables for a molecular system with an electron spectral gap, in the limit of large ratio of nuclei and electron masses, without assuming that the nuclei are localized to vanishing domains. The derivation, based on a Hamiltonian system interpretation of the Schrödinger equation and stability of the corresponding hitting time Hamilton-Jacobi equation for non ergodic dynamics, bypasses the usual separation of nuclei and electron wave functions, includes caustic states and gives a different perspective on theBorn-Oppenheimer approximation, Schrödinger Hamiltonian systems and numerical simulation in molecular dynamics modeling at constant energy.

• 30.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Bolåneräntor i Sverige: Enanalys av individuella räntor med multipel linjär regression2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

This report investigates how a number of customer-specific factors affect individual interest rates for Swedish home mortgages. The method used is multiple linear regression with transformations of the explanatory variables. Transformations that we employ are log-linear, linear-log, log-log and piecewise linear. The dataset consists of approximately 7000 Swedish home mortgages with floating interest rates from July 2013. Loan to value ratio, loan size and the the choice of mortgage lender are identified as the most important factors that influence individual interest rates. We find that large loans in combination with low loan to value ratio tend to lead to lower interest rates. There are also significant differences in interest rates depending on the mortgage lender.

• 31.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
Portfolio Optimization: Approaches to determining VaR and CVaR2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

This thesis analyses portfolio optimization using the risk measures VaR and CVaR with two different underlying assumptions of probability distribution of returns; one being that portfolio returns are normal distributed and the other being a discrete distribution comprised of historical data. The models are run through numerous historical simulations on the OMXS30 with varying time period for historical data and rebalance frequencies. The resulting simulated returns as well as the CVaR outcomes are presented, compared and discussed in order to assess which model performs the best and under what circumstances.

Our key findings is that using a discrete, historical probability distribution for optimizing a portfolio with respect to CVaR, comprised of around 320 days worth of data and using a rebalancing frequency of 20 days performs the best with respect to total return and actual CVaR. This method manages to take the fat tails of the market return distribution into account and as such successfully avoids the larger market downturns.

The results of this thesis also indicate that historical VaR optimization is inferior to CVaR optimization. However due to lack of computational power this comparison is inconclusive.

• 32.
KTH, School of Industrial Engineering and Management (ITM), Industrial Economics and Management (Dept.).
The Risk-Return Tradeoff in a Hedged, Client Driven Trading Portfolio2013Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

In post-financial crisis times, new legislation in combination with banks’ changed risk aversion has to a great extent changed the proprietary trading to client driven trading, i.e. market making or client facilitation. This type of trading complicates the risk-return dynamics, as the goal is often to minimize risk and achieve profitable commission revenues. This thesis aims to disclose the risk-return tradeoff in a client driven trading environment. This is done by investigating the conditional relation between risk and realized return. As opposed from many studies which proxy the risk with beta or variance, I use a delta-gamma Value at Risk model as the risk proxy, which I also backtest. For the return proxy, I use three different measures; P&L, commission revenues and the sum of these two. A positive tradeoff exists if (i) the return is equally negatively dependent on the risk if the ex post return is negative, as it is positively dependent on the risk if the ex post return is positive and (ii) the average return is significantly positive. For three different client driven trading portfolios tested, I found a positive risk-return tradeoff in one portfolio, between the P&L plus commission revenues and the Value at Risk. However, since a symmetrical conditional relationship between risk and P&L plus commission revenues was found in all portfolios, and the average return was positive, the positive tradeoff would have existed if the average return would have been significantly positive. On the other hand, one could argue that the tradeoff exists, but is not significant. No relation between risk and commission revenues was found. A probable cause to this is the hedging strategies, which would be an interesting topic for further research.

• 33. Beyersdorff, O.
KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.
Lower bounds: From circuits to QBF Proof Systems2016In: ITCS 2016 - Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science, Association for Computing Machinery (ACM), 2016, p. 249-260Conference paper (Refereed)

A general and long-standing belief in the proof complexity community asserts that there is a close connection between progress in lower bounds for Boolean circuits and progress in proof size lower bounds for strong propositional proof systems. Although there are famous examples where a transfer from ideas and techniques from circuit complexity to proof complexity has been effective, a formal connection between the two areas has never been established so far. Here we provide such a formal relation between lower bounds for circuit classes and lower bounds for Frege systems for quantified Boolean formulas (QBF). Starting from a propositional proof system P we exhibit a general method how to obtain a QBF proof system P + 8red, which is inspired by the transition from resolution to Qresolution. For us the most important case is a new and natural hierarchy of QBF Frege systems C-Frege + 8red that parallels the well-studied propositional hierarchy of C-Frege systems, where lines in proofs are restricted to belong to a circuit class C. Building on earlier work for resolution [Beyersdorff, Chew, and Janota, 2015a] we establish a lower bound technique via strategy extraction that transfers arbitrary lower bounds for the circuit class C to lower bounds in C-Frege + 8red. By using the full spectrum of state-of-The-Art circuit lower bounds, our new lower bound method leads to very strong lower bounds for QBF Frege systems: (i) exponential lower bounds and separations for the QBF proof system AC0[p]-Frege + 8red for all primes p; (ii) an exponential separation of AC0[p]-Frege + 8red from TC0-Frege + 8red; (iii) an exponential separation of the hierarchy of constantdepth systems AC0 d-Frege + 8red by formulas of depth independent of d. In the propositional case, all these results correspond to major open problems.

• 34.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Mapping of open-answers using machine learning2018Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

This thesis investigates if a model can be created to map misspelled answers from open-ended questions to a ﬁnite set of brands. The data used for the paper comes from the company Nepa that uses open-questions to measure brand-awareness and consists of misspelled answers and brands to be mapped to. A data structure called match candidate was created and consists of a misspelled answer and brand that it poten-tially be mapped to. Features for the match candidates were engineered and based on the edited distances, posterior probability and common misspellings among other. Multiple machine learning models were tested for classifying the match candidates as positive if the mapping was correct and negative otherwise. The model was tested in two scenarios, one when the answers in the training and testing data came from the same questions and secondly when they came from diﬀerent ones. Among the classiﬁers tested, the random forest model performed best in terms of PPV as well as sensitivity. The resulting mapping identiﬁed on average 92% of the misspelled answers and map then with 98% accuracy in the ﬁrst scenario. While in the second scenario 70% of the answers were identiﬁed with 95% conﬁdence in the mapping on average.

• 35.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Almost sure absolute continuity of Bernoulli convolutions2010In: Ann. Inst. H. Poincaré Probab. Statist., ISSN 0246-0203, Vol. 46, no 3, p. 888-893Article in journal (Refereed)

We prove an extension of a result by Peres and Solomyak on almostsure absolute continuity in a class of symmetric Bernoulli convolutions.

• 36.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Seco Points påverkan på Secos lönsamhet2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 37.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
The impact of macro-economic indicators on credit spreads2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

• 38.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Analysis of Copula Opinion Pooling with Applications to Quantitative Portfolio Management2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

In 2005 Attilio Meucci presented his article Beyond Black-Litterman: Views on Non-Normal Markets which introduces the copula opinion pooling approach using generic non-normal market assumptions. Copulas and opinion pooling are used to express views on the market which provides a posterior market distribution that smoothly blends an arbitrarily distributed market prior distribution with arbitrarily chosen views. This thesis explains how to use this method in practice and investigates its performance in different investment situations. The method is tested on three portfolios, each showing some different feature. The conclusions that can be drawn are e.g. that the method can be used in many different investment situations in many different ways, implementation and calculations can be made within a few seconds for a large data set and the method could be useful for portfolio managers using mathematical methods. The presented examples together with the method generate reasonable results.

• 39.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
Calibration of Multilateration Positioning Systems via Nonlinear Optimization2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

This master thesis presents an evaluation of a method for improving performance of sensor positioning in a network of emitters. The positioning method used for the analysis is Time Difference of Arrival, TDOA, a multilateration technique based on measurements of differences in signal travel time between a pair of synchronous and spatially separated pairs of emitters and a sensor. The method in question aims at reducing positioning errors caused by errors in initially reported emitter positions as well as network synchronization errors by using already known sensor positions to re-calibrate the network of emitters. This is done by minimizing the difference between signal based TDOA measurements from the system and estimated TDOA measurements made by calculations based on given sensor positions by means of nonlinear least squares optimization. Alterations of the method with different settings and error contributions and with varying amount of sensors and emitters are tested throughout several simulations. The proposed method shows apparent results of improving the system parameters and also copes well with contributing errors provided that the amount of measurements is sufficiently large.

• 40.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
Optimering av Schemaläggning2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

The purpose of this paper is to investigate the possibilities to use mathematical optimization when scheduling at the Retail Client Department of Carnegie Funds. The study has been executed through formulation of two mathematical models on an optimization problem for scheduling. This consists of assigning shifts based upon predetermined conditions. A linear model and a quadratic model were used to optimize the schedule, solving the problem with the computer program Matlab. The results show that the mathematical optimization of scheduling potentially could be implemented in the department since all models used guarantee approved schedules. However, the result of the quadratic model shows that it cannot guarantee optimality within reasonable time.

In addition to the technical investigation, the report covers an analysis of the parameters that the retail client manager should take into account when scheduling. This part of the report has been implemented through a literature review with focus on how managers can influence knowledge sharing within an organization, and an interview with the retail client manager. In the optimization of schedules the authors recommend organizations to dispersedly distribute shifts to employees of the Retail Client Department.

• 41.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Regression analysis as a valuation model: A case study of North American and European construction industry mergers and acquisitions2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

During a company acquisition, one of the advising investment banks’ prime tasks is to valuate the target company. The potential value of the company is usually presented during a pitch when the investment bank try to convince the company owners that they should be chosen to advise on the sale. There are numerous factors affecting the company value, both internal such as revenues and earnings, and external factors like taxes and the region of origin.

When presenting this indicative valuation to a prospective client, can multiple linear regression analysis provide a more accurate valuation than the Comparable Companies Valuation model, and how well does it fit the needs of the investment bank?

These matters are investigated by using a robust regression model based on the factors mentioned above, and the appropriateness of the model is discussed with a professional from the financial industry. The thesis concludes in that the regression model indeed provides better accuracy than the Comparable Companies Valuation model, but that it is not suitable for all clients.

• 42. Bär, Christian
KTH, Superseded Departments, Mathematics.
Surgery and the spectrum of the Dirac operator2002In: Journal für die Reine und Angewandte Mathematik, ISSN 0075-4102, E-ISSN 1435-5345, Vol. 552, p. 53-76Article in journal (Refereed)

We show that for generic Riemannian metrics on a simply-connected closed spin manifold of dimension greater than or equal to5 the dimension of the space of harmonic spinors is not larger than it must be by the index theorem. The same result holds for periodic fundamental groups of odd order. The proof is based on a surgery theorem for the Dirac spectrum which says that if one performs surgery of codimension greater than or equal to3 on a closed Riemannian spin manifold, then the Dirac spectrum changes arbitrarily little provided the metric on the manifold after surgery is chosen properly.

• 43.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Do hedge funds yield greater risk-adjusted rate of  returns than mutual funds?A quantitative study comparing hedge funds to mutual funds and hedge fund strategies2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

In recent times, the popularity of hedge funds has undoubtedly increased. There are shared opinions on whether hedge funds generate absolute rates of returns and whether they provide a strong alternative investment to mutual funds. This thesis aims to examine whether hedge funds with different investment strategies create absolute returns and if certain investment strategies outperform others. This thesis compares hedge funds risk-adjusted rate of return towards mutual funds, such as mutual funds, to see if certain investment strategies are more lucrative than the corresponding investments in terms of excess returns to corresponding indices. An econometric approach was applied to search for significant differences in risk-adjusted returns of hedge funds in contrast to mutual funds.

Our results show that Swedish hedge funds do not generate as high risk-adjusted returns as Swedish mutual funds. In regard to the best performing hedge fund strategy, the results are inconclusive. Also, we do not find any evidence that hedge funds violate the effective market hypothesis.

• 44.
Universite Paul Sabatier, Toulouse, France.
KTH, Superseded Departments, Mathematics.
The polynomial projectors that preserve homogeneous differential relations: a new characterization of Kergin interpolation2004In: East Journal on Approximations, ISSN 1310-6236, Vol. 10, no 4, p. 441-454Article in journal (Refereed)
• 45. Correggi, Michele
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Local density approximation for the almost-bosonic anyon gas2017In: Analysis & PDE, ISSN 2157-5045, E-ISSN 1948-206X, Vol. 10, no 5, p. 1169-1200Article in journal (Refereed)

We study the minimizers of an energy functional with a self-consistent magnetic field, which describes a quantum gas of almost-bosonic anyons in the average-field approximation. For the homogeneous gas we prove the existence of the thermodynamic limit of the energy at fixed effective statistics parameter, and the independence of such a limit from the shape of the domain. This result is then used in a local density approximation to derive an effective Thomas–Fermi-like model for the trapped anyon gas in the limit of a large effective statistics parameter (i.e., “less-bosonic” anyons).

• 46.
KTH, Superseded Departments, Mathematics.
Topological properties of complexes of graph homomorphisms2004Licentiate thesis, comprehensive summary (Other scientific)
• 47.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Dirac eigenvalues for generic metrics on three-manifolds2003In: Annals of Global Analysis and Geometry, ISSN 0232-704X, E-ISSN 1572-9060, Vol. 24, p. 95-100Article in journal (Refereed)

We show that for generic Riemannian metrics on a closed spin manifold of dimension three the Dirac operator has only simple eigenvalues.

• 48.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Bayesian inference methods in operational risk2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

Under the Advanced Measurement Approach (AMA), banks must use four different sources of information to assess their operational risk capital requirement. The three main quantitative sources available to build the future loss distribution are internal loss data, external loss data and scenario analysis. The fourth source, business environment and internal control factors, is treated as an ex-post update to capital calculations and is not a subject of this thesis. Ap- proaches from Extreme Value Theory (EVT) have gained popularity in the area of operational risk in recent years, with its focus on the behaviour of processes at extreme levels making it a natural candidate for operational risk modelling. However, the adoption of EVT in operational risk modelling has encountered several obstacles with the main one being the scarcity of data leading to substantial statistical uncertainty for both parameter and capital estimates. This Master thesis evaluates Bayesian Inference approaches to extreme value estimation and implements a method to reduce these uncertainties. The results indicate that the Bayesian Inference approaches gives a significant reduction of the statistical uncertainties compared to more traditional estimators and also performs well when applied on real-world data sets.

• 49.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Modelling Football as a Markov Process: Estimating transition probabilities through regression analysis and investigating it’s application to live betting markets2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

This degree thesis aims for a modeling of football set pieces (i.e Throw Ins, Free Kicks, Goal Kicks and Corners) through the use of Markov theory. By using regression analysis on a various range of covariates we will try to estimate the transition probabilities of such a process from a state to another and investigate what factors might have an impact on these probabilities. Although not reaching a sufficiently high level of variance explanation, the model constructed shows strong significance and let us believe that an articulation of it could lead to a strong model for these set pieces. Furthermore we will proceed with an analysis addressing the application of such modeling within the pricing processes of betting companies, based on a case study of Metric Gaming. Undertaking an operational management perspective, we will assess which level of implementation of such modeling is the most efficient, and what consequences it will have in two sub-perspectives; the risk management and branding of the company

• 50.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
Optimering av ett patientflöde inom svensk veterinärvård2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

This  thesis  aims  to  examine  the  patient  flow  through  the  Swedish  veterinary  clinic  Mälaren  Hästklinik.  The  thesis  also  examines  how  this  flow  can  be  improved.  The clinic  has,  as  of  today,  long  patient  queues  in  certain  parts  of  the  process,  and  a  mathematical model is made to improve this process.

Firstly, an examination of the clinic is made and suitable mathematical theories are selected. The patient flow is then modelled from this mathematical perspective and this  modelling  is  compared  to  the  reality.  Finally,  a  mathematical  improvement  of  the  patient  flow  is  made.  The  results  presented  are  that  it  is  clearly  possible  to represent the current patient flow with mathematical models and theories. It is also shown  that  there  is  some  theoretical  optimization  to  be  made  that  reduces  the  queuing time, and the total time in the system.

Lastly, there are also presented methods and theories for how a Swedish SME active in  the  veterinary  business  should  consider  an  efficiency  process  through  a  sustainability perspective.

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