The dividend function in the jump-diffusion dual model with barrier dividend strategy

被引：0
作者：
Bo Li
Rong Wu
机构：
[1] Nankai University,School of Mathematical Sciences and LPMC
来源：
Applied Mathematics and Mechanics | 2008年 / 29卷
关键词：
compound Poisson process; diffusion process; Gerber-Shiu function; integro-differential equation; time of ruin; surplus before ruin; deficit at ruin; O211.6; 60J75; 62P25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A dual model of the perturbed classical compound Poisson risk model is considered under a constant dividend barrier. A new method is used in deriving the boundary condition of the equation for the expectation function by studying the local time of a related process. We obtain the expression for the expected discount dividend function in terms of those in the corresponding perturbed compound Poisson risk model without barriers. A special case in which the gain size is phase-type distributed is illustrated. We also consider the existence of the optimal dividend level.
引用
收藏
页码：1239 / 1249
页数：10
相关论文
共 28 条
[1]  
Gerber H. U.(1970)An extension of the renewal equation and its application in the collective theory of risk[J] Skandinavisk Aktuarietidskrift 53 205-210
[2]  
Gerber H. U.(1998)On the discounted penalty at ruin in a jump-diffusion and the perpetual put option[J] Insurance: Mathematics and Economics 22 263-276
[3]  
Landry B.(2003)The time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process perturbed by diffusion[J] Insurance: Mathematics and Economics 33 59-66
[4]  
Chiu S. N.(2001)On the discounted distribution functions of the surplus process perturbed by diffusion[J] Insurance: Mathematics and Economics 28 401-419
[5]  
Yin C. C.(2003)The joint density function of three characteristics on jump-diffusion risk process[J] Insurance: Mathematics and Economics 32 445-455
[6]  
Tsai C. C. L.(1957)Su un’impostazione alternativa della teoria collettiva del rischio[C] Proceedings of the Transactions of the XV International Congress of Actuaries 2 433-443
[7]  
Zhang C.(2004)Some optimal dividends problems[J] ASTIN Bulletin 34 49-74
[8]  
Wang G.(1981)On the probability of ruin in the presence of a linear dividend barried[J] Scandinavian Actuarial Journal 2 105-115
[9]  
De Finetti B.(2004)Optimal dividends: analysis with Brownian motion[J] North American Actuarial Journal 8 1-20
[10]  
Dickson D. C. M.(2004)On a class of renewal risk models with a constant dividend barrier[J] Insurance: Mathematics and Economics 35 691-701
123