The method of successive approximations for calculating the probability of bankruptcy of a risk process in a Markovian environment

被引：2

作者：

B. V. Norkin

机构：

[1] National Academy of Sciences of Ukraine,V. M. Glushkov Institute of Cybernetics

来源：

Cybernetics and Systems Analysis | 2004年 / 40卷 / 6期

关键词：

actuarial mathematics; risk process; Markovian chain; bankruptcy probability; system of integral equations; method of successive approximations;

D O I：

10.1007/s10559-005-0031-x

中图分类号：

学科分类号：

摘要：

A generalized model of a classical risk process describing the evolution of the capital of an insurance company in a random environment is considered. A system of integral equations for the bankruptcy probability if a function of initial state. The possibility of applying the method of successive approximation to solve the system is analyzed. The method generates approximations that converge from above and below to the solution.

引用

页码：917 / 927

页数：10

共 7 条

[1]

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[2]

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[3]

Jansen J.(1985)Probabilities de ruine pour une classe de modeles de risque semi-Markoviens ASTIN Bulletin 15 123-133

[4]

Reinhard J. M.(2001)Probability of ruin with variable premium rate in a Markovian environment Insurance: Mathematics and Economics 29 291-296

[5]

Jasiulewicz E.(1969)Markovian processes homogeneous in the second component Teor. Veroyatn. i yeyo Primen. 14 3-14

[6]

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[7]

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