The maximum surplus before ruin and related problems in a jump-diffusion renewal risk process

被引:2
|
作者
Wang, Shan Shan [1 ]
Zhang, Chun Sheng [2 ,3 ]
机构
[1] Tianjin Polytech Univ, Dept Math, Tianjin 300160, Peoples R China
[2] Nankai Univ, Sch Math, Tianjin 300071, Peoples R China
[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China
基金
中国国家自然科学基金;
关键词
Sparre Andersen risk model; phase-type inter-claim times; maximum surplus before ruin; expected present value of dividends; barrier dividend strategy; diffusion; integro-differential equation; DISCOUNTED PENALTY; DIVIDEND PAYMENTS; PROBABILITIES; MODEL; TIME;
D O I
10.1007/s10114-011-9427-x
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we investigate a Sparre Andersen risk model perturbed by diffusion with phase-type inter-claim times. We mainly study the distribution of maximum surplus prior to ruin. A matrix form of integro-differential equation for this quantity is derived, and its solution can be expressed as a linear combination of particular solutions of the corresponding homogeneous integro-differential equations. By using the divided differences technique and nonnegative real part roots of Lundberg's equation, the explicit Laplace transforms of particular solutions are obtained. Specially, we can deduce closed-form results as long as the individual claim size is rationally distributed. We also give a concise matrix expression for the expected discounted dividend payments under a barrier dividend strategy. Finally, we give some examples to present our main results.
引用
收藏
页码:2379 / 2394
页数:16
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