随机利率下复合泊松模型的最优注资分红策略  

Optimal Dividend and Capital Injection Strategies in the Compound Poisson Model with Random Interest Rates

作　　者：刘伟强[1] 占梦雅[1] LIU Weiqiang;ZHAN Mengya(School of Statistics,East China Normal University,Shanghai,200062,China)

机构地区：[1]华东师范大学统计学院,上海200062

出　　处：《应用概率统计》2020年第6期627-655,共29页Chinese Journal of Applied Probability and Statistics

摘　　要：本文研究了随机利率条件下复合泊松风险模型的最优分红注资策略.模型假设盈余过程服从一般形式而利率过程随某一马尔科夫过程变化.问题通过两步得到解决.首先,找到最优策略满足的注资的形式;然后,在限定注资形式的条件下得出问题的最优解.这里,我们讨论了有界分红率和无界分红率两种分红形式,并且在索赔分布为指数分布的条件下讨论了最优解的可能形式.The paper considers the optimal dividend and capital injection strategies for the compound poisson risk process in a random interest rates environment.In the model,the surplus is assumed to be ordinary but the interest rates are governed by an exogenous Markov chain.Here,the problem is solved by two steps.First,we find out the capital injection form that the optimal strategy should follow.Then we look for the optimal solution in the restricted set with the particular capital injection form.In the paper,we discuss "restricted" and "unrestricted" two cases and provide a possible solution for "unrestricted" case when the claim distribution is exponential.

关 键 词：复合泊松风险模型 分红 注资 哈密尔顿-雅克比-贝尔曼方程 随机利率 

分 类 号：O211.62[理学—概率论与数理统计]