索赔次数为复合Poisson-Geometric过程下的破产概率和最优投资和再保险策略

Ruin Probability and Optimal Investment and Reinsurance Strategy for Insurer with Compound Poisson-Geometric Risk Process

本文对索赔次数为复合Poisson-Geometric过程的风险模型,在保险公司的盈余可以投资于风险资产,以及索赔购买比例再保险的策略下,研究使得破产概率最小的最优投资和再保险策略.通过求解相应的Hamilton-Jacobi-Bellman方程,得到使得破产概率最小的最优投资和比例再保险策略,以及最小破产概率的显示表达式.

In this paper,we consider an insurance company whose surplus （reserve） is modeled by a compound Poisson-Geometric risk process perturbed by a diffusion. The insurance company can invest part of the surplus in a risky asset and purchase proportional reinsurance for claims. We consider the optimization problem of minimizing the probability of ruin. By solving the corresponding Hamilton-Jacobi-Bellman equations, explicit expressions for the minimal ruin probability and the corresponding optimal strategies are obtained.