带比例及固定费用的对偶模型分红策略  

Optimal Dividend Payments in a Dual Risk Model with both Fixed and Proportional Costs

作　　者：陈树敏[1,2] 何春雄[3] 

机构地区：[1]肇庆学院数学与信息科学学院,肇庆526061 [2]广东工业大学自动化学院,广州510006 [3]华南理工大学理学院,广州510640

出　　处：《应用概率统计》2013年第2期136-150,共15页Chinese Journal of Applied Probability and Statistics

基　　金：广东省高等学校高层次人才项目"最优再保险;投资与分红的模型与策略研究";国家杰出青年科学基金资助项目(70825002);国家自然科学基金项目(71201173);广东省自然科学基金项目(S2012040006838);中国博士后科学基金项目(2012M510195)资助

摘　　要：本文考虑对偶风险模型的最佳分红策略问题.该模型常用于描述一类具有固定费用支出及不确定收益特点的公司企业的现金流变化.假定分红过程存在比例及固定交易费用并定义公司盈余资金首次为0时刻为破产时间,本文的目标是最大化破产之前期望累积分红的贴现值.优化问题可以通过随机脉冲控制方法进行求解.当对偶模型跳跃幅度满足指数分布时,本文通过求解相应的准变分不等式(QVI)得到值函数及最优策略的显式表达式.In this paper, we study the optimal dividend problem in a dual risk model, which might be appropriate for companies that have fixed expenses and occasional profits. Assuming that dividend payments are subject to both proportional and fixed transaction costs, our object is to maximize the expected present value of dividend payments until ruin, which is defined as the first time the company＇s surplus becomes negative. This optimization problem is formulated as a stochastic impulse control problem. By solving the corresponding quasi-variational inequality （QVI）, we obtain the analytical solutions of the value function and its corresponding optimal dividend strategy when jump sizes are exponentially distributed.

关 键 词：分红 交易费用 对偶模型 准变分不等式 随机脉冲控制 

分 类 号：O221.3[理学—运筹学与控制论]