最小化损失概率的再保险和投资问题

Optimal Proportional Reinsurance and Investment with Minimizing Ruin Probability

本文考虑保险公司的再保险和投资策略问题.为了在降低风险的同时增加收益,保险公司会考虑在再保险的基础上将剩余财富投资到m种风险资产中.资产中风险资产的价格波动服从几何布朗运动.本文给出了考虑再保险和投资之后的财富模型,基于最小化损失概率的基础上求解其相应的HJB方程,从而给出保险公司的再保险和投资的最优策略.

In this paper, we consider a problem of optimal reinsurance and investment with multiple risky assets for an insurance company whose surplus is governed by a linear diffusion. The insurance company＇s risk can be reduced through reinsurance,while,in addition,the company invests its surplus in a financial market with one risk-free asset and m risky assets. The risky assets＇ prices are governed by geometric Brownian motions. We consider the optimization problem of minimizing the ruin probability and solve it by using the corresponding Hamihon-Jacobi-Bellman（HJB） equation. Explicit expression for the optimal value function and the corresponding optimal strategies are obtained.