| 摘要 | 第1-14页 |
| Abstract | 第14-31页 |
| 1 Preliminaries | 第31-45页 |
| ·Dynamic Programming | 第31-40页 |
| ·Markov processes | 第31-32页 |
| ·Controlled Markov processes | 第32-34页 |
| ·Bellman's optimality principle | 第34-35页 |
| ·Hamilton-Jacobi-Bellman equation(HJB):formal description | 第35-38页 |
| ·The verification theorem | 第38-40页 |
| ·The Maximum Principle | 第40-41页 |
| ·Other Control Problems | 第41-45页 |
| ·Impulse control | 第41-42页 |
| ·Partial observation control problem | 第42-45页 |
| 2 Optimal Dividend Payments subject to Transaction Costs and Taxes | 第45-171页 |
| ·Optimal Excess-of-Loss Reinsurance and Dividend Payments with Both Transaction Costs and Taxes | 第45-68页 |
| ·Introduction | 第45-47页 |
| ·Problem formulation | 第47-50页 |
| ·The gain of excess-of-loss reinsurance | 第50-51页 |
| ·The quasi-variational inequalities | 第51-53页 |
| ·The solution of quasi-variational inequalities | 第53-64页 |
| ·The optimal return function and the optimal strategy | 第64-68页 |
| ·Optimal Dividend Payments in the Classical Risk Model When Payments are Subject to Both Transaction Costs and Taxes | 第68-90页 |
| ·Problem formulation | 第68-70页 |
| ·The quasi-variational inequalities and the verification theorem | 第70-75页 |
| ·The closed-form solution for exponential claim distribution | 第75-88页 |
| ·Time to ruin or to the next dividend | 第88-90页 |
| ·Optimal Dividend Policies for a General Diffusion with Transaction Costs and Solvency Constraints | 第90-128页 |
| ·Introduction | 第90-91页 |
| ·The model and a general optimality result | 第91-95页 |
| ·Optimality under payout restrictions | 第95-97页 |
| ·Optimality under solvency constraints | 第97-102页 |
| ·Numerical Solutions | 第102-105页 |
| ·Numerical examples | 第105-128页 |
| ·Optimal Dividend Policies with Transaction Costs for an Extended Family of Diffusion Processes | 第128-171页 |
| ·The model | 第128页 |
| ·The preliminary results in Case that x_λ>0 | 第128-136页 |
| ·The optimal solution in Case B | 第136-162页 |
| ·The optimal solution in Case C | 第162-165页 |
| ·The optimal solution in Case D | 第165-171页 |
| 3 Minimizing the probability of ruin and maximizing the exponential utility | 第171-229页 |
| ·Optimal Investment and Proportional Reinsurance Strategy for Claims Following Brownian Motion with Drift | 第171-195页 |
| ·Introduction | 第171-173页 |
| ·The model | 第173-174页 |
| ·Maximizing exponential utility of terminal wealth | 第174-181页 |
| ·Minimizing probability of ruin | 第181-188页 |
| ·Minimizing expected discounted penalty of ruin | 第188-195页 |
| ·Optimal proportional reinsurance and investment with multiple risky assets and no-shorting constraint | 第195-210页 |
| ·Introduction | 第195-196页 |
| ·The model | 第196-197页 |
| ·Maximizing expected exponential utility of terminal wealth | 第197-203页 |
| ·Minimizing probability of ruin | 第203-210页 |
| ·Optimal dynamic excess-of-loss reinsurance and multidimensional portfolio selection under short-selling prohibition | 第210-229页 |
| ·The model | 第210-212页 |
| ·Maximizing exponential utility of terminal wealth | 第212-219页 |
| ·Minimizing probability of ruin | 第219-227页 |
| ·Examples | 第227-229页 |
| 4 Mean-Variance Problem in Insurance | 第229-285页 |
| ·Dynamic Mean-Variance Problem with Constrained Risk Control for the Insurers | 第229-253页 |
| ·Introduction | 第229-231页 |
| ·The classical risk model | 第231-244页 |
| ·The diffusion model | 第244-253页 |
| ·Dynamic M-V Portfolio under Classical Risk Model Perturbed by Fractional Brownian Motion | 第253-266页 |
| ·Introduction | 第253-256页 |
| ·The model | 第256-258页 |
| ·Efficient strategy | 第258-263页 |
| ·Efficient frontier | 第263-266页 |
| ·Optimal Multi-Asset Investment with No-shorting Constraint | 第266-285页 |
| ·Solution to the stochastic LQ-problem | 第266-279页 |
| ·Efficient strategy and efficient frontier | 第279-285页 |
| 5 Optimal Control Problems when Risk Processes Modelled by(Fractional) Brownian Motion with Drift | 第285-311页 |
| ·Optimal Insurance Control for Insurers with Jump-Diffusion Risk Process | 第285-301页 |
| ·The model | 第285-287页 |
| ·Solution of the control problem | 第287-301页 |
| ·Insurance Control for Classical Risk Model with Fractional Brownian Motion Perturbation | 第301-311页 |
| ·Introduction | 第301-303页 |
| ·Explicit solution of control problem | 第303-311页 |
| 6 The Other Criteria | 第311-353页 |
| ·Dynamic Stochastic Cooperative Reinsurance Strategy in a Continuous Time Model | 第311-327页 |
| ·Introduction | 第311-312页 |
| ·The model | 第312-314页 |
| ·Main results | 第314-324页 |
| ·The Examples | 第324-327页 |
| ·Utility Maximization with Partial Information:the HJB Equation Approach | 第327-339页 |
| ·Introduction | 第327-328页 |
| ·The model | 第328-329页 |
| ·Solution to the control problem | 第329-339页 |
| ·Minimizing Expected Time to Reach a Given Capital before Ruin | 第339-353页 |
| ·Introduction | 第339页 |
| ·Model formulation | 第339-341页 |
| ·Minimizing expected time to reach a given capital | 第341-353页 |
| Bibliography | 第353-365页 |
| Acknowledgements | 第365-366页 |
| Resume and Publications | 第366-367页 |
