On the solution of the basic integral equation of actuarial mathematics by the method of successive approximations

被引：0

作者：

Norkin B.V. ^{[1
]}

机构：

[1] Institute of Cybernetics, Ukrainian National Academy of Sciences, Kiev

来源：

Ukrainian Mathematical Journal | 2007年 / 59卷 / 12期

关键词：

Successive Approximation; Insurance Claim; Initial Capital; Risk Process; Compound Poisson Process;

D O I：

10.1007/s11253-008-0033-8

中图分类号：

学科分类号：

摘要：

We study the basic integral equation of actuarial mathematics for the probability of (non)ruin of an insurance company regarded as a function of the initial capital. We establish necessary and sufficient conditions for the existence of a solution of this equation, general sufficient conditions for its existence and uniqueness, and conditions for the uniform convergence of the method of successive approximations for finding the solution. © 2007 Springer Science+Business Media, Inc.

引用

页码：1902 / 1913

页数：11

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