复合Poisson模型带投资-借贷利率和固定交易费用的最优分红策略  

Optimal Dividend Strategy in the Compound Poisson Model with Credit-Debit Interest and Transaction Costs and Taxes

作　　者：李静伟 刘国欣[2] LI Jingwei;LIU Guoxin(Department of Economics and Management,Tianjin Electronic Information College,Tianjin 300350,China;School of Science,Hebei University of Technology,Tianjin 300401,China)

机构地区：[1]天津电子信息职业技术学院经济与管理系,天津300350 [2]河北工业大学理学院,天津300401

出　　处：《运筹与管理》2023年第7期204-210,共7页Operations Research and Management Science

基　　金：国家自然科学基金资助项目(1207012113,11471218)。

摘　　要：本文研究了复合Poisson模型带投资-借贷利率和固定交易费用的最优分红问题。通过控制分红时刻和分红量,最大化直到绝对破产时刻的累积期望折现分红。由于考虑固定交易费用,问题为一个随机脉冲控制问题。首先,本文给出了一个策略是平稳马氏策略的充分必要条件。借助于测度值生成元理论得到测度值动态规划方程(简称测度值DPE),并且在没有任何附加条件下证明了验证定理。通过Lebesgue分解,本文讨论了测度值DPE和拟变分不等式(简称QVI)之间的关系,证明了最优分红策略为具有波段结构的平稳马氏策略。最后,本文给出了求解n-波段策略和相应值函数的算法。当索赔额服从指数分布时,得到了值函数的显示解和最优分红策略。The ability of insurance companies to pay dividends is an important indicator that reflects the company’s operating conditions and economic strength.What kind of dividend strategy is adopted affects not only the interests of shareholders,but also the stability of the company’s surplus,the liquidity of assets,the ability to debt,and even the survival of the company.Seeking the optimal dividend strategy is of course one of the important issues that the industry and theorists care about,and it is an important means of corporate risk management.DE FINETTI[1]proposed a realistic and economically motivated stability criterion:The management of the company should look for maximizing the expectation of the present value of all dividends paid to the shareholders up to ruin time.GERBER[2]first showed that an optimal dividend strategy has a band structure for the compound Poisson risk model.Since then the optimal dividend problem has been developed rapidly for the compound Poisson risk model.Due to its practical importance,the issue of absolute ruin problem has attracted attention in the actuarial literature.Ruin(negative reserve)does not mean the end of the game but only the necessity of raising additional money and that it will be a good investment to rescue a company when the situation is not too serious.We then assume that when the surplus is negative or the company is on deficit,the company could borrow money at a debit interest forceβ>0.Meanwhile,the company will repay its debt continuously from its income.Thus,the surplus of the company is driven under the debit interest forceβ>0,when the surplus is negative.We allow a company to continue its business with debt as long as it is profitable.However,when the surplus of a company is below the level-c/β,we say that absolute ruin occurs at this situation.In the compound Poisson risk model,the surplus cannot return to a positive level once it attains the critical level-c/β.In this case,the value-c/βmay be interpreted as the maximum allowable debt for a company.When

关 键 词：最优分红问题 固定交易费用 测度值DPE 马氏策略 

分 类 号：O211[理学—概率论与数理统计]