Simple approximation for the ruin probability in renewal risk model under interest force via Laguerre series expansion
Simple approximation for the ruin probability in renewal risk model under interest force via Laguerre series expansion
复制标题
利息力下更新风险模型破产概率的拉盖尔级数展开的简单近似
DOI：
10.1080/03461238.2021.1885483
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发表时间：
2021-02
影响因子：
1.8
通讯作者：
Zhimin Zhang
中科院分区：
文献类型：
--
作者：
Eric C. K. Cheung;Zhimin Zhang
尽管具有信用兴趣的更新保险风险模型中的损失概率可能被视为经典研究问题，但在索赔金额和Interlaim t is Interlaim t is Interlaim t n Interlaim t n of Crance中只能提供精确的解决方案
Although the ruin probability in a renewal insurance risk model with credit interest may be viewed as a classical research problem, exact solutions are only available in the literature in very special cases when both the claim amounts and the interclaim times follow distributions such as the exponential. This is a long standing problem especially from a computational point of view, and the difficulty lies in the fact that the ruin probability usually satisfies a higher order integro-differential equation and/or an ordinary differential equation with non-constant coefficients. In this paper, for a large class of interclaim time distributions (including a combination of exponentials), we shall develop an approximation for the ruin probability using Laguerre series expansion as a function of the initial surplus level. It is shown that the (approximated) Laguerre coefficients can be solved from a system of linear equations, a procedure that is very easy to implement. A main advantage of our approach is that no specific distributional assumption on the claim amounts is required, apart from some mild differentiability and integrability conditions that can be verified. Numerical examples are provided to illustrate the very good performance of our approximation including both light-tailed and heavy-tailed claims.
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