时滞损失相依准则下时间一致性问题的最优再保险与投资策略

Optimal Reinsurance-Investment Strategy for Time-consistent Problem with Time-lag Under Loss-dependent Criterion

在损失相依保费准则下,研究以均值-方差为目标函数的保险公司最优再保险与投资问题.假设保险公司通过购买比例再保险分散风险,同时,可以投资一个价格服从Heston随机波动率模型的风险资产,并考虑时滞效应.通过应用随机最优控制理论,给出并证明了验证定理,建立相应的拓展Hamilton-Jacobi-Bellman (HJB)方程,通过求解HJB方程,得到了保险公司最优再保险与投资策略及均衡值函数的显式解析式.最后,通过数值模拟分析了参数对最优再保险与投资策略的影响.

Under the loss-dependent premium criterion,the optimal reinsurance-investment problem of insurance companies with mean-variance as the objective function is studied.It is assumed that an insurance company diversifies the risk by purchasing proportional reinsurance,meanwhile,it can invest in a risky asset whose price obeys Heston’s stochastic volatility model and take the time-lag effect into account.Then,using the stochastic optimal control theory,the verification theorem is given and proved,and the corresponding extended Hamilton-Jacobi-Bellman(HJB)equations are established.The analytical expression of the optimal reinsurance and investment strategy and the equilibrium value function of the insurance company are obtained by solving the equations.Finally,the effects of parameters on reinsurance and investment strategies are analyzed by numerical simulation.