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