考虑违约风险的兼顾保险公司与再保险公司利益的最优投资与再保险问题研究

Optimal investment and reinsurance problem for the insurer's and the reinsurer's interests under default risk

本文主要研究了考虑违约风险的兼顾保险公司与再保险公司共同利益的最优投资与再保险问题.假设索赔过程由带漂移的几何布朗运动描述,保险公司可以投资于一无风险资产、一支股票和一可违约债券,再保险公司可以投资于一无风险资产和一支股票.以两家公司终端财富的期望指数效用乘积最大为目标,采用随机控制理论建立优化问题对应的HJB方程,进而分别得到违约前和违约后的最优策略和价值函数.最后本文分析了各模型参数对最优投资和再保险策略的影响,并给出相应的经济解释.

This paper considers an optimal investment and reinsurance problem involving a defaultable security for a group which holds shares of an insurance company and a reinsurance company.Assuming that the claim process is described by a Brownian motion with drift,the insurer can purchase proportional reinsurance and invest a risk-free asset,a stock and a defaultable bond,and the reinsurer can invest a risk-free asset and a stock.Taking both the insurer and the reinsurer into account,this paper aims to maximize the expected product of the insurer's and the reinsurer's exponential utilities of terminal wealth.By using the techniques of stochastic control theory,the corresponding Hamilton-Jacobi-Bellman(HJB)equations are established for the pre-default case and post-default case,respectively.In both cases,closed-form expressions for the optimal strategies and the corresponding value functions are derived.Finally,numerical examples are given to illustrate the effects of model parameters on the optimal investment and reinsurance strategies,and the corresponding economic explanations are given.