Optimal Portfolio Strategies On Survival And Growth Problems For The Common Shock Risk Model

In this dissertation,goal-reaching problems regarding optimal investment and proportional reinsurance are studied from the perspective of the insurance company.We employ compound poisson and diffusion models to describe the wealth process and discuss two insurance business that are correlated with a common shock.Both survival problems in danger-zone where the wealth level is below a critical value and growth problems in safe-region where the wealth level is above a critical value are investigated.There is a probability of bankruptcy in danger-zone but it can be avoided in the safe-region.Therefore,the two main objectives are to maximize the probability of reaching the safe-region before ruin and minimize the expected time of hitting the goal once safe-region is achieved.The problem is first discussed under the multidimensional financial market framework,and by applying dynamic programming principle,we derive the Hamilton-Jacobi-Bellman equation.Then,the analytical solutions to the optimal strategies and value functions with constraints on reinsurance strategies are provided in dimension reduced market framework.It is shown that the optimal strategy for the survival problem does not exist.But it is possible to modify it and construct an ?-optimal(suboptimal)strategy to maximize the probability of crossing the barrier and reach the safe-region before ruin.Finally,to investigate the influence of some typical parameters on the optimal strategies and ?-optimal(suboptimal)strategy,we present the numerical simulation and analysis.