| 中文摘要 | 第4-7页 |
| Abstract | 第7-10页 |
| Notation | 第14-15页 |
| Chapter 1 Preliminaries | 第15-23页 |
| 1.1 Sublinear expectation | 第15-16页 |
| 1.2 G-Brownian motion | 第16-21页 |
| 1.3 G-L(?)vy process | 第21-23页 |
| Chapter 2 A stochastic maximum principle for processes driven byG-Brownian motion and applications to finance | 第23-45页 |
| 2.1 Introduction | 第23-26页 |
| 2.2 Stochastic optimal control problem under G-expectation | 第26-28页 |
| 2.3 Variational equations and their moment estimationunder G-expectation | 第28-33页 |
| 2.4 Adjoint processes and the maximum principle | 第33-37页 |
| 2.5 Sufficient conditions of optimality | 第37-40页 |
| 2.6 Applications to finance | 第40-44页 |
| 2.7 Conclusion | 第44-45页 |
| Chapter 3 Upper bounds for ruin probabilities under model uncertainty | 第45-57页 |
| 3.1 Introduction | 第45-47页 |
| 3.2 Problem formulation | 第47-49页 |
| 3.3 Two-sided ruin problem | 第49-52页 |
| 3.4 Optimal investment strategy and ruin probability | 第52-57页 |
| Chapter 4 Maximum principle for Markov regime-switching forward-backward stochastic control system with jumps andrelation to dynamic programming | 第57-83页 |
| 4.1 Introduction | 第57-59页 |
| 4.2 Formulation of the optimal control problems | 第59-61页 |
| 4.3 A sufficient stochastic maximum principle | 第61-64页 |
| 4.4 Relation to dynamic programming | 第64-73页 |
| 4.5 Applications to finance | 第73-82页 |
| 4.5.1 Maximum principle approach | 第75-80页 |
| 4.5.2 Dynamic programming approach | 第80-82页 |
| 4.5.3 Relationship | 第82页 |
| 4.6 Conclusion | 第82-83页 |
| Chapter 5 Optimal mean-variance investment and reinsurance problems foran insurer with stochastic volatility | 第83-99页 |
| 5.1 Introduction | 第83-85页 |
| 5.2 The model | 第85-88页 |
| 5.2.1 Some notations | 第85-86页 |
| 5.2.2 Problem formulation | 第86-88页 |
| 5.3 Solution to the unconstrained problem: BSDE approach | 第88-93页 |
| 5.4 Efficient strategy and efficient frontier | 第93-94页 |
| 5.5 Sensitivity analysis | 第94-97页 |
| 5.6 Conclusion | 第97-99页 |
| Chapter 6 A risk-sensitive maximum principle for a Markovregime-switching jump-diffusion system and applications | 第99-133页 |
| 6.1 Introduction | 第99-101页 |
| 6.2 Formulation of the optimal control problems | 第101-103页 |
| 6.3 Statement of risk-sensitive maximum principle | 第103-107页 |
| 6.4 Proofs of the main results | 第107-119页 |
| 6.5 Applications | 第119-130页 |
| 6.5.1 Application to LQ risk-sensitive control under regime-switching | 第119-122页 |
| 6.5.2 Application to risk-sensitive benchmarked asset management underregime-switching | 第122-130页 |
| 6.6 Conclusion | 第130-133页 |
| Bibliography | 第133-143页 |
| Resume and Publications | 第143-144页 |
