Numerical computation of Gerber-Shiu function for insurance surplus process with additional investment

被引:0
|
作者
Punaluek, Sutipon [1 ]
Imamura, Yuri [2 ]
机构
[1] Chulalongkorn Univ, Fac Sci, Dept Math & Comp Sci, Bangkok 10330, Thailand
[2] Kanazawa Univ, Inst Sci & Engn, Fac Math & Phys, Kanazawa 9201192, Japan
来源
关键词
Risk model; insurance surplus process; investment; Bachelier model; ruin probability; Gerber-Shiu function; JUMP-DIFFUSION; RUIN;
D O I
10.1142/S2661335223500107
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper studies the Gerber-Shiu function for the insurance surplus process with additional investment under the Bachelier model. The Gerber-Shiu function allows us to study the moments of the time of ruin, which is the first time that the surplus is negative. First, we use the martingale theory in deriving the integro-differential equation of the Gerber-Shiu function. Then, we give the exact solution of the ruin probability in case the amount of claims follows the exponential distribution. Under a general distribution case, we propose a numerical method of the Gerber-Shiu function using the finite differential method based on the integro-differential equation. Then, numeric illustrations are provided to study the effect of the parameters on the Gerber-Shiu function.
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页数:7
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