复合Poisson模型带比例与固定交易费用的最优分红与注资  

Optimal dividend payment and capital injection of the compound Poisson risk model with both proportional and fixed costs

作　　者：张帅琪[1] 刘国欣[2] 

机构地区：[1]中南大学数学科学与计算技术学院,长沙410075 [2]河北工业大学理学院,天津300130

出　　处：《中国科学：数学》2012年第8期827-843,共17页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:10971048)资助项目

摘　　要：研究了复合Poisson模型带比例与固定费用的最优分红与注资问题.每次分红与注资时,存在比例及固定的交易费用.通过控制分红与注资的时刻以及分红及注资量,实现破产前分红减注资的折现期望的最大化.由于存在固定交易费用,问题为一个脉冲控制问题.根据问题的参数不同,问题的解可分为两大类.一类解为只进行最优分红不需要注资,而另一类情况需要注资.需要注资时,最优注资策略由最优注资上界以及最优注资下界描述.当赤字小于最优注资下界的绝对值时,进行注资.最后,在理赔为指数分布时明确地给出了两类共七种最优策略以及值函数的形式.从而彻底地解决了该问题.This paper deals with the optimal dividend payment risk model. With each dividend payment and capital injection and capital injection problem for the classical there is a proportional cost and a fixed cost. It controls the timing and the amount of both dividends paid out and equity issuance. The objective of the corporation is to maximize the expected discounted dividends payout minus the equity issuance until the time of bankruptcy. Due to the presence of the fixed transaction costs with each dividend payment and capital injection, the problem is formulated as an impulse stochastic control problem. It turns out that the control problem is associated with qualitatively different optimal capital injection strategies, depending on the problem＇s data. One allows for no capital injection and the other allows for capital injection. We solve this problem explicitly in the case of exponential claim amount distributions. It is shown that there can be essentially seven different solutions depending on the model＇s parameters and the costs.

关 键 词：最优分红策略注资 拟变分不等式 随机脉冲控制 

分 类 号：O231.3[理学—运筹学与控制论] F840.32[理学—数学]