A Note on a Generalized Gerber–Shiu Discounted Penalty Function for a Compound Poisson Risk Model

Jiechang Ruan, Wenguang Yu, Ke Song, Yihan Sun, Yujuan Huang and Xinliang Yu
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Jiechang Ruan: Department of Humanities and Social Sciences, Yibin Vocational & Technical College, Yibin 644003, China
Wenguang Yu: School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China
Ke Song: School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China
Yihan Sun: School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China
Yujuan Huang: School of Science, Shandong Jiaotong University, Jinan 250357, China
Xinliang Yu: School of Insurance, Shandong University of Finance and Economics, Jinan 250014, China

Mathematics, 2019, vol. 7, issue 10, 1-12

Abstract: In this paper, we propose a new generalized Gerber–Shiu discounted penalty function for a compound Poisson risk model, which can be used to study the moments of the ruin time. First, by taking derivatives with respect to the original Gerber–Shiu discounted penalty function, we construct a relation between the original Gerber–Shiu discounted penalty function and our new generalized Gerber–Shiu discounted penalty function. Next, we use Laplace transform to derive a defective renewal equation for the generalized Gerber–Shiu discounted penalty function, and give a recursive method for solving the equation. Finally, when the claim amounts obey the exponential distribution, we give some explicit expressions for the generalized Gerber–Shiu discounted penalty function. Numerical illustrations are also given to study the effect of the parameters on the generalized Gerber–Shiu discounted penalty function.

Keywords: compound Poisson risk model; generalized Gerber–Shiu discounted penalty function; Laplace transform; Dickson–Hipp operator; recursive formula (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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