| Titre : | Stochastic maximum principle for system governed by forward backward stochastic differential equation with risk sensitive control problem and application |
| Auteurs : | Rania Khallout, 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, 2019 |
| Format : | 1 vol. (96 p.) / 30 cm |
| Langues: | Anglais |
| Mots-clés: | Fully coupled forward backward stochastic differential equation,Optimal control,Risk-sensitive,Necessary Optimality Conditions,Sufficient Optimality Conditions,Mean variance,Cash flow. |
| Résumé : | Throughout this thesis, we focused our aim on the problem of optimal control under a risk-sensitive performance functional, where the systems studied are given by a backward stochastic differential equation, fully coupled forward-backward stochastic differential equation, and fully coupled forward backward stochastic differential equation with jump. As a preliminary step, we use the risk neutral which is an extension of the initial control system where the set of admissible controls are convex in all the control problems, and an optimal solution exists. Then, we study the necessary as well as sufficient optimality conditions for risk sensitive performance, we illustrate our main results by giving applied examples of risk sensitive control problem. The first is under linear stochastic dynamics with exponential quadratic cost function. The second example deals with an optimal portfolio choice problem in financial market specially the model of control cash flow of a firm or project. The last one is an example of mean-variance for risk sensitive control problem applied in cash flow market. |
| Sommaire : |
Acknowledgement i
Abstract ii Résumé iii Table of Contents iv Symbols and Abbreviations vi Introduction 1 1 Expected exponential utility and Girsanov’s theorem 6 1.1 Problem formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Financial market of the risk-sensitive . . . . . . . . . . . . . . . . . . . . . . 8 1.2.1 Factor dynamic without jump diffusion . . . . . . . . . . . . . . . . . 8 1.2.2 Factor dynamic with jump diffusion process . . . . . . . . . . . . . . 13 1.2.3 Mean-Variance of loss functional . . . . . . . . . . . . . . . . . . . . . 28 2 Pontryagin’s risk-sensitive stochastic maximum principle for fully coupled FBSDE with applications 31 2.1 Formulation of the problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.2 Risk-sensitive stochastic maximum principle of fully coupled forward-backward control problem type . . . . . . .. 34 2.2.1 How to find the new adjoint equation ? . . . . . . . . . . . . . . . . . 37 2.3 Risk sensitive sufficient optimality conditions . . . . . . . . . . . . . . . . . . 47 2.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.4.1 Example 01: Application to the linear quadratic risk-sensitive control problem . . . . . . 52 2.4.2 Example 02: Application to risk sensitive stochastic optimal portfolio problem . . . . . . . 55 2.4.3 Solution of the deterministic functions A(t) and B (t) via Riccati equation 59 3 Pontryagin’s risk-sensitive stochastic maximum principle for fully coupled FBSDE with jump diffusion and finantial application 62 3.1 Problem formulation and assumptions . . . . . . . . . . . . . . . . . . . . . . 62 3.2 Risk-neutral necessary optimality conditions . . . . . . . . . . . . . . . . . . 66 3.2.1 Steps to …nd the transformed adjoint equation . . . . . . . . . . . . . 70 3.3 Risk sensitive sufficient optimality conditions . . . . . . . . . . . . . . . . . . 81 3.4 Example: Mean-Variance (Cash-flow) . . . . . . . . . . . . . . . . . . . . . . 84 Conclusion and Perspectives 90 Bibliography 92 |
| En ligne : | http://thesis.univ-biskra.dz/4492/1/Th%C3%A9se_Rania-khalout.pdf |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| TM/94 | Théses de doctorat | bibliothèque sciences exactes | Consultable |
