| Titre : | Stochastic Maximum Principle for the System Governed by Backward Doubly Stochastic Differential Equations with Risk-Sensitive Control Problem and Applications |
| Auteurs : | HAFAYED Dahbia, Auteur ; Adel Chala, Directeur de thèse |
| Type de document : | Monographie imprimée |
| Editeur : | Biskra [Algérie] : Faculté des Sciences Exactes et des Sciences de la Nature et de la Vie, Université Mohamed Khider, 2020 |
| Format : | 1 vol. (90 p.) / couv. ill. en coul / 30cm |
| Langues: | Anglais |
| Mots-clés: | Backward doubly stochastic differential equation,fully coupled forward-backward stochastic differential equation of mean-field,risk-sensitive,stochastic maximum principle,variational principle,Logarithmic transformation. |
| Résumé : |
This 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. |
| Sommaire : |
Contents
Abstract vi Résumé vii Symbols and Abbreviations viii General Introduction 1 1 Basic Notations of Expected Exponential Utility and Related Field 8 1.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Expected Exponential Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Financial Market of the Risk-Sensitive . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.4 Mean-Variance of Loss Functional . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2 ARisk-Sensitive Stochastic Maximum Principle for Backward Doubly Stochastic Differential Equations with Application 23 2.1 Formulation of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2 Risk-Sensitive Stochastic Maximum Principle of Backward Doubly Type Control . 27 2.3 New Adjoint Equations and Risk-sensitive Necessary Optimality Conditions . . . 30 2.4 Risk-Sensitive Sufficient Optimality Conditions . . . . . . . . . . . . . . . . . . . . 38 2.5 Applications: A Linear Quadratic Risk-Sensitive Control Problem . . . . . . . . . . 41iv CONTENTS 2.5.1 Example 01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.5.2 Example 02 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3 ARisk-Sensitive Stochastic Maximum Principle for Fully Coupled Forward-Backward Stochastic Differential Equations of Mean-Field Type with Application 52 3.1 Problem Formulation and Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.2 Relation between the Risk-Neutral and Risk-Sensitive Stochastic Maximum Principle 57 3.3 New Adjoint Equations and Risk-Sensitive Necessary Optimality Conditions . . . 61 3.4 Risk-Sensitive Sufficient Optimality Conditions . . . . . . . . . . . . . . . . . . . . 70 3.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.5.1 Example 1: Risk-Sensitive Control Applied to the Mean-Field Linear-Quadratic 74 3.5.2 Example 2: Financial Application: Mean-Variance Risk-Sensitive Stochastic Optimal Portfolio Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 77 General Conclusion 84 Bibliography |
| En ligne : | http://thesis.univ-biskra.dz/5113/1/HAFAYED_Dahbia_Thesis.pdf |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| TM/104 | Théses de doctorat | bibliothèque sciences exactes | Empruntable |
