Dahbia, HAFAYED
(2020)
*Stochastic Maximum Principle for the System Governed by
Backward Doubly Stochastic Differential Equations with
Risk-Sensitive Control Problem and Applications.*
Doctoral thesis, Université de mohamed kheider biskra.

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## Abstract

his thesis based on the study of the stochastic maximum principle with risk-sensitive for two different systems. We obtain these systems by generalizing the results of Chala [10; 11], and by using the paper of Djehiche et al. in [13]: The first system is driven by a backward doubly stochastic differential equation. We use the risk-neutral model for which an optimal solution exists as a preliminary step, this is an extension of the initial control problem. Our goal is to establish necessary and sufficient optimality conditions for the risk-sensitive performance functional control problem. We show for the second system which is driven by a fully coupled forward-backward stochastic differential equation of mean-field type, by using the same technique as in the first case, we get the necessary and sufficient optimality conditions for the risk-sensitive, where the set of admissible controls is convex in all the cases. Finally, we illustrate our main results by giving applied examples of risk-sensitive control problems.

Item Type: | Thesis (Doctoral) |
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Uncontrolled Keywords: | Backward doubly stochastic differential equation, fully coupled forward-backward stochastic differential equation of mean-field, risk-sensitive, stochastic maximum principle, variational principle, Logarithmic transformation. |

Subjects: | Q Science > QA Mathematics |

Divisions: | Faculté des Sciences Exactes et des Sciences de la Nature et de la Vie > Département de Mathématiques |

Depositing User: | BFSE |

Date Deposited: | 02 Dec 2020 08:12 |

Last Modified: | 02 Dec 2020 08:12 |

URI: | http://thesis.univ-biskra.dz/id/eprint/5113 |

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