| 中文摘要 | 第1-11页 |
| ABSTRACT | 第11-14页 |
| Chapter 1 Preliminaries | 第14-22页 |
| §1.1 Some basic risk models | 第14-19页 |
| §1.2 About optimal dividend problems | 第19-20页 |
| §1.3 Confluent hypergeometric equation | 第20-22页 |
| Chapter 2 Dividend payments in the classical risk model under absolute ruin | 第22-43页 |
| §2.1 Introduction | 第22-23页 |
| §2.2 Moment generating function of D_(u,b) | 第23-26页 |
| §2.3 Moments of D_(u,b) | 第26-27页 |
| §2.4 Explicit expressions for exponential claims | 第27-31页 |
| §2.5 Optimal dividend barrier for exponential claims | 第31-35页 |
| §2.6 Numerical analysis for Erlang(2) claim sizes | 第35-36页 |
| §2.7 The Gerber-Shiu expected discounted penalty function | 第36-43页 |
| Chapter 3 Optimal dividends in the classical risk model with credit and debit interests under absolute ruin | 第43-57页 |
| §3.1 Introduction | 第43-44页 |
| §3.2 Moment generating function of D_(u,b) | 第44-45页 |
| §3.3 Moments of D_(u,b) | 第45-46页 |
| §3.4 Explicit expressions of M_(u, y; b) and V_n(u, b) | 第46-51页 |
| §3.5 Optimal choice of dividend barrier for exponential claims | 第51-53页 |
| §3.6 The Laplace transform of absolute ruin time | 第53-57页 |
| Chapter 4 The perturbed compound Poisson risk process with in vestment and debit interest | 第57-78页 |
| §4.1 Introduction | 第57-58页 |
| §4.2 The stochastic Dirichlet problem | 第58-60页 |
| §4.3 Integro-differential equations | 第60-62页 |
| §4.4 Integral equations | 第62-65页 |
| §4.5 A renewal equation and asymptotic results for Φ_+ | 第65-69页 |
| §4.6 Explicit results for exponential claims Φ_+ | 第69-78页 |
| Chapter 5 On the perturbed compound Poisson risk model under absolute ruin with debit interest and a constant dividend barrier | 第78-96页 |
| §5.1 Introduction | 第78-79页 |
| §5.2 Integro-differential equations for V_1(u, b) | 第79-82页 |
| §5.3 Moment generating function and higher moments of D_(u,b) | 第82-88页 |
| §5.4 The Gerber-Shiu expected discounted penalty function | 第88-96页 |
| Chapter 6 Optimal dividend strategy in the perturbed compound Poisson risk model with investment interest | 第96-113页 |
| §6.1 Introduction | 第96-97页 |
| §6.2 Hamilton-Jacobi-Bellman equation | 第97-102页 |
| §6.3 Construction of the optimal strategy | 第102-108页 |
| §6.4 Examples | 第108-113页 |
| Chapter 7 Optimality of the barrier strategy for spectrally negative Levy risk processes | 第113-126页 |
| §7.1 Introduction | 第113-115页 |
| §7.2 Preliminaries on log-convex functions and related functions | 第115-118页 |
| §7.3 Convex solutions for integro-differential equations | 第118-123页 |
| §7.4 The optimality of the barrier strategy | 第123-126页 |
| References | 第126-134页 |
| Acknowledgements | 第134页 |
