方差保费原则下具有违约风险的均值-方差保险者的时间一致最优投资和再保险问题（英文）

本文研究在均值-方差准则下保险者的最优投资再保险策略问题,其中保险者可以投资到无风险资产,股票和违约债券上,股票服从Heston模型.保险者可以购买比例再保险或者得到新的保险业务,特别地,保险和再保险的保费通过方差保费原则来计算.通过使用博弈论方法,我们分别解决了违约前和违约后的扩展的HJB方程并且得到了相应的时间一致最优投资再保险策略表达式.最后,我们用数值例子来说明模型参数对最优策略的影响.

Time-Consistent Investment and Reinsurance Problems for Mean-Variance Insurers with Default Risk Under Variance Premium Principle

In this paper, we consider an optimal investment-reinsurance strategy problem under mean-variance criterion for an insurer, who can trade in a risk-free asset, a stock whose price process is described by Heston model and a defaultable bond. The insurer can purchase proportional reinsurance or acquire new insurance business. In particular, we assume that the premium of insurance and reinsurance are calculated through the variance premium principle. Applying game theoretic perspective, we solve the extended Hamilton-Jacobi-Bellman (HJB) equations and derive optimal time-consistent investmentreinsurance strategies for the pre-default case and the post-default case, respectively. Finally, numerical simulations are provided to analyze the impact of model parameters on the optimal reinsurance and investment strategies.