风险模型中带贵的比例再保险和交易费用的最优分红和融资控制问题（英文）  

The Optimal Dividend and Financing Control Problem in the Risk Model with Non-cheap Proportional Reinsurance and Transaction Costs

作　　者：刘烨[1] 马世霞[1] Liu Ye Ma Shixia(School of Sciences, Hebei University of Technology, Tianjin 300401, China)

机构地区：[1]河北工业大学理学院,天津300401

出　　处：《南开大学学报（自然科学版）》2016年第6期29-39,共11页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：Supported by the Natural Science Foundation of China(11301133,11471218);the Natural Sciences Foundation of Hebei province(A2014202236,A2014202052)

摘　　要：研究了风险模型中贵的比例再保险和交易费用下的最优分红和融资控制问题,找到破产前使股东分红减去融资额的现值期望最大的策略.考虑了两种交易费用和贵的比例再保险,并且通过构造两类次最优控制模型解决最优控制问题.最终证明出两类次最优模型中的解是所要求的最优策略下的值函数.The optimal dividend and financing control problem with non-cheap proportional reinsurance and transaction costs in the risk model is studied.In the model,the objective is to find the strategy which maximizes the expected present value of the dividends payout minus the equity issuance until the time of ruin.The optimal control problem with two kinds of transaction costs and non-cheap proportional reinsurance by constructing two categories of suboptimal control models is solved.Finally,it is verified that the value function and the optimal strategy with the corresponding solution in either category of suboptimal models.

关 键 词：分红 融资 贵的比例再保险 HJB方程 最优策略 

分 类 号：O232[理学—运筹学与控制论]