交易费用影响下带扰动对偶模型的最优分红与注资策略

Optimal dividend and capital injection strategies for a perturbed dual model with transaction costs

考虑带扰动的对偶风险模型的最优分红与注资控制问题,分红与注资都带有比例费用,同时分红还带有固定费用,保险公司的目标为最大化期望折现分红与折现注资之差.当收入额满足指数分布时,该优化问题可以通过随机脉冲控制方法解决,通过求解相应的拟变分不等式,得到值函数的显式解和最优双边界策略.最后通过数值算例讨论了扰动、注资与分红的交易费用对值函数和双边界的影响.

The optimal dividend and capital injection control problem of dual risk model with perturbations are considered,in which dividend and capital injection have proportional costs,and dividend also has fixed costs.The objective of insurance company is to maximize the expected discounted dividends minus the discounted capital injections.When the income sizes follow an exponential distribution,the optimization problem can be solved by means of random pulse control,so the closed-form of the value function and the optimal two-barrier policy are obtained by solving the corresponding quasi-variational inequalities.Finally,numerical examples are given to study the influences of perturbation,transaction costs of capital injection and dividend on the value function and dividend boundary.