On the Gerber-Shiu function with random discount rate

被引：4

作者：

Wang, Houchun ^{[1
]}

Ling, Nengxiang ^{[2
]}

机构：

[1] Anhui Jianzhu Univ, Sch Math & Phys, Hefei 230601, Peoples R China

[2] Hefei Univ Technol, Sch Math, Hefei, Peoples R China

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2017年 / 46卷 / 01期

关键词：

Asymptotic formula; Gerber-Shiu function; Random discount rate; Renewal equation; POISSON RISK MODEL; DEFECTIVE RENEWAL EQUATION; DIVIDEND BARRIER; PENALTY-FUNCTION; RUIN; TIME; DIFFUSION; SURPLUS;

D O I：

10.1080/03610926.2014.988265

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, we study the Gerber-Shiu (G-S) function for the classical risk model, in which the discount rate is generalized from a constant to a random variable. The discounted interest force accumulated process is modeled by a Poisson process and a Gaussian process for the G-S function. In terms of the standard techniques in ruin theory, we derive the integro-differential equation and the defective renewal equation satisfied by the G-S function. Then, the asymptotic formula for the G-S function is obtained using the renewal theory.

引用

页码：210 / 220

页数：11

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