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  • 1. Agram, N.
    et al.
    Haadem, S.
    Øksendal, B.
    Proske, F.
    A Maximum Principle for Infinite Horizon Delay Equations2013Inngår i: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 45, nr 4, s. 2499-2522Artikkel i tidsskrift (Fagfellevurdert)
  • 2.
    Agram, Nacira
    Department of Mathematics, University of Oslo, Oslo, Norway;;University of Biskra, Biskra, Algeria.
    Dynamic risk measure for BSVIE with jumps and semimartingale issues2019Inngår i: Stochastic Analysis and Applications, ISSN 0736-2994, E-ISSN 1532-9356, Vol. 37, nr 3, s. 361-376Artikkel i tidsskrift (Fagfellevurdert)
  • 3. Agram, Nacira
    Stochastic optimal control of McKean–Vlasov equations with anticipating law2019Inngår i: Afrika Matematika, ISSN 1012-9405, E-ISSN 2190-7668, Vol. 30, nr 5-6, s. 879-901Artikkel i tidsskrift (Fagfellevurdert)
  • 4. Agram, Nacira
    et al.
    Bachouch, Achref
    Øksendal, Bernt
    Proske, Frank
    Singular Control Optimal Stopping of Memory Mean-Field Processes2019Inngår i: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 51, nr 1, s. 450-468Artikkel i tidsskrift (Fagfellevurdert)
  • 5. Agram, Nacira
    et al.
    Bakdi, Azzeddine
    Oksendal, Bernt
    Deep Learning and Stochastic Mean-Field Control for a Neural Network ModelManuskript (preprint) (Annet vitenskapelig)
  • 6.
    Agram, Nacira
    et al.
    Department of Mathematics, Linnaeus University (LNU), Växjö, Sweden.
    Choutri, Salah Eddine
    Learning and Game Theory Laboratory (L&G-Lab), New York University Abu Dhabi, Abu Dhabi, UAE;Center for Stability, Instability, and Turbulence (SITE), New York University Abu Dhabi, Abu Dhabi, UAE.
    Mean-field FBSDE and optimal control2020Inngår i: Stochastic Analysis and Applications, ISSN 0736-2994, E-ISSN 1532-9356, Vol. 39, nr 2, s. 235-251Artikkel i tidsskrift (Fagfellevurdert)
  • 7. Agram, Nacira
    et al.
    Haadem, S.
    Øksendal, B.
    Proske, F.
    Optimal Stopping, Randomized Stopping, and Singular Control with General Information Flow2022Inngår i: Theory of Probability and its Applications, ISSN 0040-585X, E-ISSN 1095-7219, Vol. 66, nr 4, s. 601-612Artikkel i tidsskrift (Fagfellevurdert)
  • 8.
    Agram, Nacira
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Hu, Yaozhong
    Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada..
    oksendal, Bernt
    Univ Oslo, Dept Math, POB 1053, N-0316 Oslo, Norway..
    Mean-field backward stochastic differential equations and applications2022Inngår i: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 162, artikkel-id 105196Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we study the linear mean-field backward stochastic differential equations (mean-field BSDE) of the form & nbsp;& nbsp;{dY(t) = -[alpha(1)(t)Y(t) +& nbsp;beta(1)(t)Z(t) +& nbsp;integral(R0 & nbsp;)eta(1)(t,& nbsp;zeta)K(t,& nbsp;zeta)nu(d zeta) +& nbsp;alpha(2)(t)E[Y(t)] +& nbsp;beta(2)(t)E[Z(t)] +& nbsp;integral(R0 & nbsp;)eta(2)(t,& nbsp;zeta)E[K(t,& nbsp;zeta)]nu(d zeta) +& nbsp;gamma(t)]dt + Z(t)dB(t) +& nbsp;integral K-R0 (t,& nbsp;zeta)(N) over tilde(dt, d zeta), t & nbsp;is an element of & nbsp;[0, T].Y(T) =xi.& nbsp;& nbsp;where (Y, Z, K) is the unknown solution triplet, B is a Brownian motion, (N) over tilde is a compensated Poisson random measure, independent of B. We prove the existence and uniqueness of the solution triplet (Y, Z, K) of such systems. Then we give an explicit formula for the first component Y(t) by using partial Malliavin derivatives. To illustrate our result we apply them to study a mean-field recursive utility optimization problem in finance.

  • 9.
    Agram, Nacira
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Labed, Saloua
    Univ Mohamed Khider Biskra, Biskra, Algeria..
    Oksendal, Bernt
    Univ Oslo, Dept Math, POB 1053, N-0316 Oslo, Norway..
    Yakhlef, Samia
    Univ Mohamed Khider Biskra, Biskra, Algeria..
    Singular Control Of Stochastic Volterra Integral Equations2022Inngår i: Acta Mathematica Scientia, ISSN 0252-9602, E-ISSN 1003-3998, Vol. 42, nr 3, s. 1003-1017Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    This paper deals with optimal combined singular and regular controls for stochastic Volterra integral equations, where the solution X-u,X-xi(t) =X(t) is given by X(t) = phi(t) + integral(t)(0) b (t, s, X(s), u(s)) ds + integral(t)(0) sigma (t, s, X(s), u(s)) dB(s) + integral(t )(0)h (t, s) d xi(s). Here dB(s) denotes the Brownian motion Ito type differential, xi denotes the singular control (singular in time t with respect to Lebesgue measure) and u denotes the regular control (absolutely continuous with respect to Lebesgue measure). Such systems may for example be used to model harvesting of populations with memory, where X(t) represents the population density at time t, and the singular control process xi represents the harvesting effort rate. The total income from the harvesting is represented by J(u, xi) = E[integral(T)(0) f(0)(t, X(t), u(t))dt + integral(T)(0) f(1)(t, X(t))d xi(t) + g(X(T))], for the given functions f(0), f(1) and g, where T > 0 is a constant denoting the terminal time of the harvesting. Note that it is important to allow the controls to be singular, because in some cases the optimal controls are of this type. Using Hida-Malliavin calculus, we prove sufficient conditions and necessary conditions of optimality of controls. As a consequence, we obtain a new type of backward stochastic Volterra integral equations with singular drift. Finally, to illustrate our results, we apply them to discuss optimal harvesting problems with possibly density dependent prices.

  • 10.
    Agram, Nacira
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Pucci, Giulia
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Øksendal, Bernt
    Impulse Control of Conditional McKean–Vlasov Jump Diffusions2024Inngår i: Journal of Optimization Theory and Applications, ISSN 0022-3239, E-ISSN 1573-2878, Vol. 200, nr 3, s. 1100-1130Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we consider impulse control problems involving conditional McKean–Vlasov jump diffusions, with the common noise coming from the σ-algebra generated by the first components of a Brownian motion and an independent compensated Poisson random measure. We first study the well-posedness of the conditional McKean–Vlasov stochastic differential equations (SDEs) with jumps. Then, we prove the associated Fokker–Planck stochastic partial differential equation (SPDE) with jumps. Next, we establish a verification theorem for impulse control problems involving conditional McKean–Vlasov jump diffusions. We obtain a Markovian system by combining the state equation with the associated Fokker–Planck SPDE for the conditional law of the state. Then we derive sufficient variational inequalities for a function to be the value function of the impulse control problem, and for an impulse control to be the optimal control. We illustrate our results by applying them to the study of an optimal stream of dividends under transaction costs. We obtain the solution explicitly by finding a function and an associated impulse control, which satisfy the verification theorem.

  • 11. Agram, Nacira
    et al.
    Røse, Elin Engen
    Optimal control of forward–backward mean-field stochastic delayed systems2017Inngår i: Afrika Matematika, ISSN 1012-9405, E-ISSN 2190-7668, Vol. 29, nr 1-2, s. 149-174Artikkel i tidsskrift (Fagfellevurdert)
  • 12. Agram, Nacira
    et al.
    Øksendal, Bernt
    A financial market with singular drift and no arbitrage2020Inngår i: Mathematics and Financial Economics, ISSN 1862-9679, E-ISSN 1862-9660, Vol. 15, nr 3, s. 477-500Artikkel i tidsskrift (Fagfellevurdert)
  • 13.
    Agram, Nacira
    et al.
    Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, N-0316 Oslo, Norway;University of Biskra, Algeria.
    Øksendal, Bernt
    Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, N-0316 Oslo, Norway.
    A Hida–Malliavin white noise calculus approach to optimal control2018Inngår i: Infinite Dimensional Analysis Quantum Probability and Related Topics, ISSN 0219-0257, Vol. 21, nr 03, s. 1850014-1850014Artikkel i tidsskrift (Fagfellevurdert)
  • 14. Agram, Nacira
    et al.
    Øksendal, Bernt
    Infinite horizon optimal control of forward–backward stochastic differential equations with delay2014Inngår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 259, s. 336-349Artikkel i tidsskrift (Fagfellevurdert)
  • 15. Agram, Nacira
    et al.
    Øksendal, Bernt
    Malliavin Calculus and Optimal Control of Stochastic Volterra Equations2015Inngår i: Journal of Optimization Theory and Applications, ISSN 0022-3239, E-ISSN 1573-2878, Vol. 167, nr 3, s. 1070-1094Artikkel i tidsskrift (Fagfellevurdert)
  • 16.
    Agram, Nacira
    et al.
    Department of Mathematics, University of Oslo, Oslo, Norway;Department of Mathematics, Linnaeus University (LNU), Växjö, Sweden.
    Øksendal, Bernt
    Department of Mathematics, University of Oslo, Oslo, Norway.
    Mean-field stochastic control with elephant memory in finite and infinite time horizon2019Inngår i: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 91, nr 7, s. 1041-1066Artikkel i tidsskrift (Fagfellevurdert)
  • 17.
    Agram, Nacira
    et al.
    Department of Mathematics, University of Oslo, Oslo, Norway;;University of Biskra, Biskra, Algeria.
    Øksendal, Bernt
    Department of Mathematics, University of Oslo, Oslo, Norway;.
    Model uncertainty stochastic mean-field control2019Inngår i: Stochastic Analysis and Applications, ISSN 0736-2994, E-ISSN 1532-9356, Vol. 37, nr 1, s. 36-56Artikkel i tidsskrift (Fagfellevurdert)
  • 18.
    Agram, Nacira
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Øksendal, Bernt
    Department of Mathematics, University of Oslo, Norway.
    Optimal stopping of conditional McKean–Vlasov jump diffusions2024Inngår i: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 188, artikkel-id 105815Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The purpose of this paper is to study the optimal stopping problem of conditional McKean–Vlasov (mean-field) stochastic differential equations with jumps (conditional McKean–Vlasov jump diffusions, for short). We obtain sufficient variational inequalities for a function to be the value function of such a problem and for a stopping time to be optimal.

    The key is that we combine the conditional McKean–Vlasov equation with the associated stochastic Fokker–Planck partial integro-differential equation for the conditional law of the state. This leads to a Markovian system which can be handled by using a version of a Dynkin formula.

    Our verification result is illustrated by finding the optimal time to sell in a market with common noise and jumps.

  • 19. Agram, Nacira
    et al.
    Øksendal, Bernt
    Stochastic Control of Memory Mean-Field Processes2017Inngår i: Applied mathematics and optimization, ISSN 0095-4616, E-ISSN 1432-0606, Vol. 79, nr 1, s. 181-204Artikkel i tidsskrift (Fagfellevurdert)
  • 20.
    Agram, Nacira
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Øksendal, Bernt
    Department of Mathematics, University of Oslo, Oslo, Norway.
    Stochastic Fokker-Planck equations for conditional McKean-Vlasov jump diffusions and applications to optimal control2023Inngår i: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 61, nr 3, s. 1472-1493Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The purpose of this paper is to study optimal control of conditional McKean-Vlasov (mean-field) stochastic differential equations with jumps (conditional McKean-Vlasov jump diffu-sions, for short). To this end, we first prove a stochastic Fokker-Planck equation for the conditional law of the solution of such equations. Combining this equation with the original state equation, we obtain a Markovian system for the state and its conditional law. Furthermore, we apply this to formulate a Hamilton-Jacobi-Bellman equation for the optimal control of conditional McKean-Vlasov jump diffusions. Then we study the situation when the law is absolutely continuous with respect to Lebesgue measure. In that case the Fokker-Planck equation reduces to a stochastic par-tial differential equation for the Radon-Nikodym derivative of the conditional law. Finally we apply these results to solve explicitly the linear-quadratic optimal control problem of conditional stochastic McKean-Vlasov jump diffusions, and optimal consumption from a cash flow.

  • 21.
    Agram, Nacira
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Øksendal, Bernt
    Department of Mathematics, University of Oslo, Oslo, Norway.
    The Donsker delta function and local time for McKean–Vlasov processes and applications2023Inngår i: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, s. 1-18Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The purpose of this paper is to establish a stochastic differential equation for the Donsker delta measure of the solution of a McKean–Vlasov (mean-field) stochastic differential equation. If the Donsker delta measure is absolutely continuous with respect to Lebesgue measure, then its Radon–Nikodym derivative is called the Donsker delta function. In that case it can be proved that the local time of such a process is simply the integral with respect to time of the Donsker delta function. Therefore we also get an equation for the local time of such a process. For some particular McKean–Vlasov processes, we find explicit expressions for their Donsker delta functions and hence for their local times. 

  • 22.
    Agram, Nacira
    et al.
    Department of Mathematics, University of Oslo, Oslo, Norway;University Mohamed Khider of Biskra, Biskra, Algeria.
    Øksendal, Bernt
    Department of Mathematics, University of Oslo, Oslo, Norway.
    Yakhlef, Samia
    University Mohamed Khider of Biskra, Biskra, Algeria.
    New approach to optimal control of stochastic Volterra integral equations2018Inngår i: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 91, nr 6, s. 873-894Artikkel i tidsskrift (Fagfellevurdert)
  • 23. Jeanblanc, Monique
    et al.
    Lim, Thomas
    Agram, Nacira
    Some existence results for advanced backward stochastic differential equations with a jump time2017Inngår i: ESAIM: Proceedings and Surveys, E-ISSN 2267-3059, Vol. 56, s. 88-110Artikkel i tidsskrift (Fagfellevurdert)
  • 24.
    Makhlouf, K.
    et al.
    Univ Biskra, Dept Math, Biskra, Algeria..
    Agram, Nacira
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Hilbert, A.
    Linnaeus Univ LNU, Dept Math, Växjö, Sweden..
    oksendal, B.
    Univ Oslo, Dept Math, Oslo, Norway..
    SPDEs with space interactions and application to population modelling2023Inngår i: ESAIM: Control, Optimisation and Calculus of Variations , ISSN 1292-8119, E-ISSN 1262-3377, Vol. 29, artikkel-id 18Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider optimal control of a new type of non-local stochastic partial differential equations (SPDEs). The SPDEs have space interactions, in the sense that the dynamics of the system at time t and position in space x also depend on the space-mean of values at neighbouring points. This is a model with many applications, e.g. to population growth studies and epidemiology. We prove the existence and uniqueness of strong, smooth solutions of a class of SPDEs with space interactions, and we show that, under some conditions, the solutions are positive for all times if the initial values are. Sufficient and necessary maximum principles for the optimal control of such systems are derived. Finally, we apply the results to study an optimal vaccine strategy problem for an epidemic by modelling the population density as a space-mean stochastic reaction-diffusion equation.

1 - 24 of 24
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