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Agram, Nacira
Publications (10 of 17) Show all publications
Agram, N. (2019). Dynamic risk measure for BSVIE with jumps and semimartingale issues. Stochastic Analysis and Applications, 37(3), 361-376
Open this publication in new window or tab >>Dynamic risk measure for BSVIE with jumps and semimartingale issues
2019 (English)In: Stochastic Analysis and Applications, ISSN 0736-2994, E-ISSN 1532-9356, Vol. 37, no 3, p. 361-376Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Taylor & Francis, 2019
National Category
Other Mathematics
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-82252 (URN)10.1080/07362994.2019.1569531 (DOI)
Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-05-06Bibliographically approved
Agram, N. & Oksendal, B. (2019). Mean-field stochastic control with elephant memory in finite and infinite time horizon. Stochastics: An International Journal of Probablitiy and Stochastic Processes, 91(7), 1041-1066
Open this publication in new window or tab >>Mean-field stochastic control with elephant memory in finite and infinite time horizon
2019 (English)In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 91, no 7, p. 1041-1066Article in journal (Refereed) Published
Abstract [en]

Our purpose of this paper is to study stochastic control problems for systems driven by mean-field stochastic differential equations with elephant memory, in the sense that the system (like the elephants) never forgets its history. We study both the finite horizon case and the infinite time horizon case. In the finite horizon case, results about existence and uniqueness of solutions of such a system are given. Moreover, we prove sufficient as well as necessary stochastic maximum principles for the optimal control of such systems. We apply our results to solve a mean-field linear quadratic control problem. For infinite horizon, we derive sufficient and necessary maximum principles. As an illustration, we solve an optimal consumption problem from a cash flow modelled by an elephant memory mean-field system.

Place, publisher, year, edition, pages
Taylor & Francis Group, 2019
Keywords
Mean-field stochastic differential equation, memory, stochastic maximum principle, partial information, backward stochastic differential equation
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-87061 (URN)10.1080/17442508.2019.1635600 (DOI)000476441900001 ()
Available from: 2019-08-01 Created: 2019-08-01 Last updated: 2019-12-06Bibliographically approved
Agram, N. & Oksendal, B. (2019). Model uncertainty stochastic mean-field control. Stochastic Analysis and Applications, 37(1), 36-56
Open this publication in new window or tab >>Model uncertainty stochastic mean-field control
2019 (English)In: Stochastic Analysis and Applications, ISSN 0736-2994, E-ISSN 1532-9356, Vol. 37, no 1, p. 36-56Article in journal (Refereed) Published
Abstract [en]

We consider the problem of optimal control of a mean-field stochasticdifferential equation (SDE) under model uncertainty. The model uncertaintyis represented by ambiguity about the law LðXðtÞÞ of the stateX(t) at time t. For example, it could be the law LPðXðtÞÞ of X(t) withrespect to the given, underlying probability measure P. This is the classicalcase when there is no model uncertainty. But it could also be thelaw LQðXðtÞÞ with respect to some other probability measure Q or,more generally, any random measure lðtÞ on R with total mass 1. Werepresent this model uncertainty control problem as a stochastic differentialgame of a mean-field related type SDE with two players. Thecontrol of one of the players, representing the uncertainty of the lawof the state, is a measure-valued stochastic process lðtÞ and the controlof the other player is a classical real-valued stochastic process u(t).This optimal control problem with respect to random probability processeslðtÞ in a non-Markovian setting is a new type of stochastic controlproblems that has not been studied before. By constructing a newHilbert space M of measures, we obtain a sufficient and a necessarymaximum principles for Nash equilibria for such games in the generalnonzero-sum case, and for saddle points in zero-sum games. As anapplication we find an explicit solution of the problem of optimal consumptionunder model uncertainty of a cash flow described by amean-field related type SDE.

Place, publisher, year, edition, pages
Taylor & Francis Group, 2019
National Category
Probability Theory and Statistics
Research subject
Mathematics, Mathematics; Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-82260 (URN)10.1080/07362994.2018.1499036 (DOI)
Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-05-06Bibliographically approved
Agram, N., Øksendal, B. & Yakhlef, S. (2019). New approach to optimal control of stochastic Volterra integral equations. Stochastics: An International Journal of Probablitiy and Stochastic Processes, 91(6), 873-894
Open this publication in new window or tab >>New approach to optimal control of stochastic Volterra integral equations
2019 (English)In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 91, no 6, p. 873-894Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Abingdon-on-Thames: Taylor & Francis, 2019
Keywords
Stochastic maximum principle, stochastic Volterra integral equation (SVIE), backward stochastic Volterra integral equation (BSVIE), Hida-Malliavin calculus, Volterra recursive utility, optimal consumption from an SVIE cash flow
National Category
Other Mathematics
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-82262 (URN)10.1080/17442508.2018.1557186 (DOI)
Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-08-09Bibliographically approved
Agram, N., Hilbert, A. & Øksendal, B. (2019). Singular control of SPDEs with space-mean dynamics. Mathematical Control & Related Fields
Open this publication in new window or tab >>Singular control of SPDEs with space-mean dynamics
2019 (English)In: Mathematical Control & Related Fields, ISSN 2156-8472Article in journal (Refereed) Epub ahead of print
Abstract [en]

We consider the problem of optimal singular control of a stochastic partial differential equation (SPDE) with space-mean dependence. Such systems are proposed as models for population growth in a random environment. We obtain sufficient and necessary maximum principles for such control problems. The corresponding adjoint equation is a reflected backward stochastic partial differential equation (BSPDE) with space-mean dependence. We prove existence and uniqueness results for such equations. As an application we study optimal harvesting from a population modelled as an SPDE with space-mean dependence.

National Category
Computational Mathematics
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-82304 (URN)10.3934/mcrf.2020004 (DOI)
Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-12-06
Agram, N., Bachouch, A., Oksendal, B. & Proske, F. (2019). Singular Control Optimal Stopping of Memory Mean-Field Processes. SIAM Journal on Mathematical Analysis, 51(1), 450-468
Open this publication in new window or tab >>Singular Control Optimal Stopping of Memory Mean-Field Processes
2019 (English)In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 51, no 1, p. 450-468Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2019
National Category
Other Mathematics
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-82261 (URN)10.1137/18M1174787 (DOI)
Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-05-06Bibliographically approved
Agram, N. & Øksendal, B. (2019). Stochastic control of memory mean-field processes. Applied mathematics and optimization, 79(1), 181-204
Open this publication in new window or tab >>Stochastic control of memory mean-field processes
2019 (English)In: Applied mathematics and optimization, ISSN 0095-4616, E-ISSN 1432-0606, Vol. 79, no 1, p. 181-204Article in journal (Refereed) Published
Abstract [en]

By a memory mean-field process we mean the solution X(&#x22C5;)" 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&lt;t." role="presentation">s<t. Our purpose is to study stochastic control problems of memory mean-field processes. We consider the space M" role="presentation">M of measures on R" role="presentation">R with the norm ||&#x22C5;||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.

Place, publisher, year, edition, pages
Springer, 2019
National Category
Other Mathematics
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-82256 (URN)10.1007/s00245-017-9425-1 (DOI)
Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-05-07Bibliographically approved
Agram, N. (2019). Stochastic optimal control of McKean-Vlasov equations with anticipating law. Afrika Matematika, 30(5-6), 879-901
Open this publication in new window or tab >>Stochastic optimal control of McKean-Vlasov equations with anticipating law
2019 (English)In: Afrika Matematika, ISSN 1012-9405, E-ISSN 2190-7668, Vol. 30, no 5-6, p. 879-901Article in journal (Refereed) Published
Abstract [en]

We are interested in Pontryagin’s stochastic maximum principle of controlled McKean–Vlasov stochastic differential equations. We allow the law to be anticipating, in the sense that, the coefficients (the drift and the diffusion coefficients) depend not only of the solution at the current time t, but also on the law of the future values of the solution PX(t+&#x03B4;)" role="presentation">PX(t+δ), for a given positive constant &#x03B4;" role="presentation">δ. We emphasise that being anticipating w.r.t. the law of the solution process does not mean being anticipative in the sense that it anticipates the driving Brownian motion. As an adjoint equation, a new type of delayed backward stochastic differential equations (BSDE) with implicit terminal condition is obtained. By using that the expectation of any random variable is a function of its law, our BSDE can be written in a simple form. Then, we prove existence and uniqueness of the solution of the delayed BSDE with implicit terminal value, i.e. with terminal value being a function of the law of the solution itself.

Place, publisher, year, edition, pages
Springer, 2019
National Category
Other Mathematics
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-82298 (URN)10.1007/s13370-019-00689-w (DOI)000481806000015 ()
Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-09-24Bibliographically approved
Agram, N. & Øksendal, B. (2018). A Hida-Malliavin white noise calculus approach to optimal control. Infinite Dimensional Analysis Quantum Probability and Related Topics, 21(3), Article ID 1850014.
Open this publication in new window or tab >>A Hida-Malliavin white noise calculus approach to optimal control
2018 (English)In: Infinite Dimensional Analysis Quantum Probability and Related Topics, ISSN 0219-0257, Vol. 21, no 3, article id 1850014Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
World Scientific, 2018
National Category
Other Mathematics
Identifiers
urn:nbn:se:lnu:diva-82296 (URN)10.1142/S0219025718500145 (DOI)
Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-05-06Bibliographically approved
Agram, N. & Engen Rose, E. (2018). Optimal control of forward–backward mean-field stochastic delayed systems. Afrika Matematika, 29(1-2), 149-174
Open this publication in new window or tab >>Optimal control of forward–backward mean-field stochastic delayed systems
2018 (English)In: Afrika Matematika, ISSN 1012-9405, E-ISSN 2190-7668, Vol. 29, no 1-2, p. 149-174Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Springer, 2018
National Category
Mathematics Other Mathematics
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-82294 (URN)10.1007/s13370-017-0532-6 (DOI)
Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-05-06Bibliographically approved
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