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.
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页码：1902 / 1913
页数：11
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