投资和再保险策略下保险公司的最优合并时刻问题

本文考虑的是允许采用比例再保险策略和投资策略的两个保险公司如何寻找最优合并时刻的问题.两个保险公司的风险过程由漂移布朗运动刻画,目标为最大化它们的生存概率.各个公司的安全负荷系数和波动系数在决定两公司是否要合并时起到了关键作用.决定合并后,公司合并费用,合并前后公司的生存概率状况在决定最优合并时刻时起到了关键作用.我们分两种情况讨论了这个问题并分别给出相应情况下的最优策略和值函数.

The Optimal Merging Problem for Two First-line Insurers with Investment and Reinsurance Policies

We consider the optimal time of merger for two first-line insurers with investment and proportional reinsurance policies. The risk processes of the two insurers are modeled by drifted Brownian motions and the objective is to maximize the survival probability of the two insurers. The safety loadings and variation coefficients of insurers play an important role in deciding whether to merge. If they decide to merge, the cost of the merger and the relation of survival probabilities before and after merger play an important role in deciding the merging time. We divide the problem into two cases. In both cases, we can get the optimal strategies and the value functions finally.