| Titre : | A second order maximum principle for singular optimal stochastic control in the classical sense |
| Auteurs : | Mayssa Zaidi, Auteur ; Abdelhak Ghoul, Directeur de thèse |
| Editeur : | Biskra [Algérie] : Faculté des Sciences Exactes et des Sciences de la Nature et de la Vie, Université Mohamed Khider, 2024 |
| Format : | 1 vol. (45 p.) / couv. ill. en coul / 30cm |
| Langues: | Anglais |
| Mots-clés: | Stochastic optimal control , SDE ( Stochastic Differential Equation). needle variation, variational equation, adjoint equation. |
| Résumé : |
In this work, we establish second-order necessary conditions for singular optimal controls in the classical sense, we consider the convex case, i.e., the control region is allowed to be convex, and the control variable enters into both the drift and the diffusion terms of the control systems. By introducing two vatariational equations and two adjoint equations, we obtain the desired necessary conditions for stochastic singular optimal controls in integral form and in martingale forms |
| Sommaire : |
Contents Remerciements ii Table of Contents iii Symbols and Acronyms v Introduction 1 1 Reminder of stochastic calculs 3 1.1 Probability space . . . . . . . . . .. . . 3 1.2 Stochastic process . . . . . . . . . . . . . . . . . . . . . 4 1.3 Brawnian motion . . . . . . . . . . . . . . . . 1.5 Stochastic integral . . . . . . . . . . . . . . . . . . . . . . 6 1.6 Stochastic di§ertential equation(SDE) . . . . . . . . . . . . . . 8 1.7 Itoís formula . . . . . . . . . . . . . . . . 10 1.7.1 Inequality . . . . . . . . . . . . . . . . . . . . . . . 11 2 Stochastic optimal control problems 13 2.1 Strong formulation . . . . . . . . . . . . . . 13 2.2 Weak formulation . . . . . . . . . . . . . .. . 14 2.3 Stochastic maximum principale . . . . . . . . . . . . . . . . 15 2.3.1 Problem formulation . . . . . . . . . . . . . . . . . 15 2.3.2 Optimal control and Optimal trajectory: . . . . . . . . . 17 2.3.3 Estimation and linearization of the solution . . . . . . . . . . . . . 18 2.3.4 Variational inequality . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3 Second order necessary conditions for singular stochastic optimal control 23 3.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . 23 3.1.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . .. . 25 3.2 Second order necessary condition in integral form . . . . .. . . 26 3.3 Martingale terms of second order maximum principle . . . . . . 37 Conclusion 44 Bibliographie 45 |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| MM/1287 | Mémoire master | bibliothèque sciences exactes | Consultable |
