Gerber-Shiu function of a discrete risk model with and without a constant dividend barrier

doi:10.1007/s11464-014-0409-z

Front. Math. China

2015, Vol. 10

Issue (2) : 377-393 https://doi.org/10.1007/s11464-014-0409-z

RESEARCH ARTICLE

Gerber-Shiu function of a discrete risk model with and without a constant dividend barrier

Shanshan WANG^1,^*(

),Chuangji AN²,Chunsheng ZHANG²

1. Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China
2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China

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Abstract

We consider the discrete risk model with exponential claim sizes. We derive the finite explicit elementary expression for the joint density function of three characteristics: the time of ruin, the surplus immediately before ruin, and the deficit at ruin. By using the explicit joint density function, we give a concise expression for the Gerber-Shiu function with no dividends. Finally, we obtain an integral equation for the Gerber-Shiu function under the barrier dividend strategy. The solution can be expressed as a combination of the Gerber-Shiu function without dividends and the solution of the corresponding homogeneous integral equation. This latter function is given clearly by means of the Gerber-Shiu function without dividends.

Keywords Discrete risk model Gerber-Shiu function time of ruin surplus before ruin deficit at ruin dividend

Corresponding Author(s): Shanshan WANG

Issue Date: 12 February 2015

Cite this article:

Shanshan WANG,Chuangji AN,Chunsheng ZHANG. Gerber-Shiu function of a discrete risk model with and without a constant dividend barrier[J]. Front. Math. China, 2015, 10(2): 377-393.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-014-0409-z
https://academic.hep.com.cn/fmc/EN/Y2015/V10/I2/377

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