| 1. |
- Agram, Nacira, 1987-, et al.
(författare)
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Optimal control of forward–backward mean-field stochastic delayed systems
- 2018
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Ingår i: Afrika Matematika. - : Springer. - 1012-9405 .- 2190-7668. ; 29:1-2, s. 149-174
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Tidskriftsartikel (refereegranskat)abstract
- We study methods for solving stochastic control problems of systems offorward–backward mean-field equations with delay, in finite and infinite time horizon.Necessary and sufficient maximum principles under partial information are given. The resultsare applied to solve a mean-field recursive utility optimal problem.
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| 2. |
- Agram, Nacira, 1987-, et al.
(författare)
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Singular Control Optimal Stopping of Memory Mean-Field Processes
- 2019
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Ingår i: SIAM Journal on Mathematical Analysis. - : Society for Industrial and Applied Mathematics. - 0036-1410 .- 1095-7154. ; 51:1, s. 450-468
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Tidskriftsartikel (refereegranskat)abstract
- The purpose of this paper is to study the following topics and the relation between them: (i) Optimal singular control of mean-field stochastic differential equations with memory; (ii) reflected advanced mean-field backward stochastic differential equations; and (iii) optimal stopping of mean-field stochastic differential equations. More specifically, we do the following: (1) We prove the existence and uniqueness of the solutions of some reflected advanced memory backward stochastic differential equations; (2) we give sufficient and necessary conditions for an optimal singular control of a memory mean-field stochastic differential equation (MMSDE) with partial information; and (3) we deduce a relation between the optimal singular control of an MMSDE and the optimal stopping of such processes.
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| 3. |
- Agram, Nacira, 1987-, et al.
(författare)
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A Hida-Malliavin white noise calculus approach to optimal control
- 2018
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Ingår i: Infinite Dimensional Analysis Quantum Probability and Related Topics. - : World Scientific. - 0219-0257. ; 21:3
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Tidskriftsartikel (refereegranskat)abstract
- The classical maximum principle for optimal stochastic control states that if a control û is optimal, then the corresponding Hamiltonian has a maximum at u = û. The first proofs for this result assumed that the control did not enter the diffusion coefficient. Moreover, it was assumed that there were no jumps in the system. Subsequently, it was discovered by Shige Peng (still assuming no jumps) that one could also allow the diffusion coefficient to depend on the control, provided that the corresponding adjoint backward stochastic differential equation (BSDE) for the first-order derivative was extended to include an extra BSDE for the second-order derivatives. In this paper, we present an alternative approach based on Hida-Malliavin calculus and white noise theory. This enables us to handle the general case with jumps, allowing both the diffusion coefficient and the jump coefficient to depend on the control, and we do not need the extra BSDE with second-order derivatives. The result is illustrated by an example of a constrained linear-quadratic optimal control.
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| 4. |
- Agram, Nacira, 1987-, et al.
(författare)
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A maximum principle for infinite horizon delay equations
- 2013
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Ingår i: SIAM Journal on Mathematical Analysis. - : Society for Industrial and Applied Mathematics. - 0036-1410 .- 1095-7154. ; 45:4, s. 2499-2522
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Tidskriftsartikel (refereegranskat)abstract
- We prove a maximum principle of optimal control of stochastic delay equations on infinite horizon. We establish first and second sufficient stochastic maximum principles as well as necessary conditions for that problem. We illustrate our results with an application to the optimal consumption rate from an economic quantity.
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| 5. |
- Agram, Nacira, 1987-
(författare)
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Dynamic risk measure for BSVIE with jumps and semimartingale issues
- 2019
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Ingår i: Stochastic Analysis and Applications. - : Taylor & Francis. - 0736-2994 .- 1532-9356. ; 37:3, s. 361-376
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Tidskriftsartikel (refereegranskat)abstract
- Risk measure is a fundamental concept in finance and in the insuranceindustry. It is used to adjust life insurance rates. In this article,we will study dynamic risk measures by means of backward stochasticVolterra integral equations (BSVIEs) with jumps. We prove a comparisontheorem for such a type of equations. Since the solution of aBSVIEs is not a semimartingale in general, we will discuss some particularsemimartingale issues.
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| 6. |
- Agram, Nacira, 1987-, et al.
(författare)
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Infinite horizon optimal control of forward–backward stochastic differential equations with delay
- 2014
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier. - 0377-0427 .- 1879-1778. ; 259:Part B, s. 336-349
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Tidskriftsartikel (refereegranskat)abstract
- We consider a problem of optimal control of an infinite horizon system governed by forward–backward stochastic differential equations with delay. Sufficient and necessary maximum principles for optimal control under partial information in infinite horizon are derived. We illustrate our results by an application to a problem of optimal consumption with respect to recursive utility from a cash flow with delay.
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| 7. |
- Agram, Nacira, 1987-, et al.
(författare)
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Introduction to White Noise, Hida-Malliavin Calculus and Applications
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- The purpose of these lectures is threefold: We first give a short survey of the Hida white noise calculus, and in this context we introduce the Hida-Malliavin derivative as a stochastic gradient with values in the Hida stochastic distribution space (S. We show that this Hida-Malliavin derivative defined on L2(FT,P) is a natural extension of the classical Malliavin derivative defined on the subspace D1,2 of L2(P). The Hida-Malliavin calculus allows us to prove new results under weaker assumptions than could be obtained by the classical theory. In particular, we prove the following: (i) A general integration by parts formula and duality theorem for Skorohod integrals, (ii) a generalised fundamental theorem of stochastic calculus, and (iii) a general Clark-Ocone theorem, valid for all F∈L2(FT,P). As applications of the above theory we prove the following: A general representation theorem for backward stochastic differential equations with jumps, in terms of Hida-Malliavin derivatives; a general stochastic maximum principle for optimal control; backward stochastic Volterra integral equations; optimal control of stochastic Volterra integral equations and other stochastic systems.
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| 8. |
- Agram, Nacira, 1987-, et al.
(författare)
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Malliavin calculus and optimal control of stochastic Volterra equations
- 2015
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Ingår i: Journal of Optimization Theory and Applications. - : Springer. - 0022-3239 .- 1573-2878. ; 167:3, s. 1070-1094
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Tidskriftsartikel (refereegranskat)abstract
- Solutions of stochastic Volterra (integral) equations are not Markov processes, and therefore, classical methods, such as dynamic programming, cannot be used to study optimal control problems for such equations. However, we show that using Malliavin calculus, it is possible to formulate modified functional types of maximum principle suitable for such systems. This principle also applies to situations where the controller has only partial information available to base her decisions upon. We present both a Mangasarian sufficient condition and a Pontryagin-type maximum principle of this type, and then, we use the results to study some specific examples. In particular, we solve an optimal portfolio problem in a financial market model with memory.
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| 9. |
- Agram, Nacira, 1987-, et al.
(författare)
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New approach to optimal control of stochastic Volterra integral equations
- 2019
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Ingår i: Stochastics. - Abingdon-on-Thames : Taylor & Francis. - 1744-2508 .- 1744-2516. ; 91:6, s. 873-894
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Tidskriftsartikel (refereegranskat)abstract
- We study optimal control of stochastic Volterra integral equations(SVIE) with jumps by using Hida-Malliavin calculus.• We give conditions under which there exist unique solutions ofsuch equations.• Then we prove both a sufficient maximum principle (a verificationtheorem) and a necessary maximum principle via Hida-Malliavincalculus.• As an application we solve a problem of optimal consumptionfrom a cash flow modelled by an SVIE.
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| 10. |
- Agram, Nacira, 1987-, et al.
(författare)
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Stochastic control of memory mean-field processes
- 2019
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Ingår i: Applied mathematics and optimization. - : Springer. - 0095-4616 .- 1432-0606. ; 79:1, s. 181-204
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Tidskriftsartikel (refereegranskat)abstract
- By a memory mean-field process we mean the solution X(⋅)" role="presentation">X(⋅) of a stochastic mean-field equation involving not just the current state X(t) and its law L(X(t))" role="presentation">L(X(t)) at time t, but also the state values X(s) and its law L(X(s))" role="presentation">L(X(s)) at some previous times s<t." role="presentation">sM of measures on R" role="presentation">R with the norm ||⋅||M" role="presentation">||⋅||M introduced by Agram and Øksendal (Model uncertainty stochastic mean-field control. arXiv:1611.01385v5, [2]), and prove the existence and uniqueness of solutions of memory mean-field stochastic functional differential equations. We prove two stochastic maximum principles, one sufficient (a verification theorem) and one necessary, both under partial information. The corresponding equations for the adjoint variables are a pair of (time-advanced backward stochastic differential equations (absdes), one of them with values in the space of bounded linear functionals on path segment spaces. As an application of our methods, we solve a memory mean–variance problem as well as a linear–quadratic problem of a memory process.
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