均值-方差准则下保险公司带内幕信息的时间一致投资-再保险策略

Time-Consistent Investment-Reinsurance Strategies for a Mean-Variance Insurer with Inside Information

文章研究在拥有内幕信息时保险公司的时间一致投资-再保险策略.假设保险公司的盈余过程为跳-扩散过程,证券市场由一个无风险资产和一个风险资产组成,且保险盈余过程与风险资产价格过程相关.从交易开始,保险公司掌握一些有关未来时刻风险资产价格的内幕信息,该信息受噪声扰动.运用滤子扩张技术将内幕信息下保险公司的财富过程进行转化.在动态均值-方差准则下,通过求解扩展的HJB方程组得到时间一致均衡投资-再保险策略以及均衡值函数的显式解,并给出相应的有效前沿.最后运用数值模拟方法分析了内幕信息及模型参数对均衡策略及有效前沿的影响.

This paper studies the time-consistent investment-reinsurance strategy for a mean-variance insurer with inside information.We assume that the surplus process of the insurer is a jump diffusion process,the stock market consists of a riskfree asset and a risky asset,and the insurer's surplus process and the risky asset price process are correlated.From the beginning of the transaction,the insurer has some inside information about the risky asset price in the future,which is disturbed by noise.The filtration expansion technique is used to transform the insurer's wealth process with inside information.Under the dynamic mean-variance criterion,by solving the extended HJB equations,the explicit solutions for the time-consistent equilibrium investment-reinsurance strategy and the equilibrium value function are derived,and the corresponding effective frontier is presented.Finally,the numerical simulation method is used to analyze the influences of the inside information and the model parameters on the optimal strategy and the effective frontier.