Refinements of two-sided bounds for renewal equations

被引：5
|
作者：
Woo, Jae-Kyung [1 ]
机构：
[1] Concordia Univ, Dept Math & Stat, Montreal, PQ H3G 1M8, Canada
来源：
INSURANCE MATHEMATICS & ECONOMICS | 2011年 / 48卷 / 02期
关键词：
(Defective) Renewal equation; Reliability classification (DFR; MWU; NWUC; NWUE); Adjustment coefficient; Nonexponential bound; JOINT DISTRIBUTION; SURPLUS PRIOR; RUIN; DISTRIBUTIONS; DEFICIT;
D O I：
10.1016/j.insmatheco.2010.10.013
中图分类号：
F [经济];
学科分类号：
02 ;
摘要：
Many quantities of interest in the study of renewal processes may be expressed as the solution to a special type of integral equation known as a renewal equation. The main purpose of this paper is to provide bounds for the solution of renewal equations based on various reliability classifications. Exponential and nonexponential types of inequalities are derived. In particular, two-sided bounds with specific reliability conditions become sharp. Finally, some examples including ultimate ruin for the classical Poisson model with time-dependent claim sizes, the joint distribution of the surplus prior to and at ruin, and the excess life time, are provided. (C) 2010 Elsevier B.V. All rights reserved.
引用
收藏
页码：189 / 196
页数：8
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