数学与统计学院学术报告[2020] 099号

(高水平大学建设系列报452号)

报告题目: Simple approximation for the ruin probability in renewal risk model under interest force via Laguerre series expansion

报告人：　 张志民　　教授  （ 重庆大学）

报告时间：2020年11月19日10：00 – 11：00

报告平台及链接： 腾讯会议ID: 766 　618 　884

报告内容：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 inte-rclaim 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, where the Laguerre coefficients do not depend on the initial surplus. 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 integrality 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.

报告人简历：张志民，重庆大学教授、博士生导师，重庆市学术技术带头人。主要研究兴趣为风险管理与精算学、金融统计、金融数学模型、非参数统计等。目前已经发表SCI或SSCI论文50余篇，且多篇发表在精算核心杂志IME、SAJ上。作为项目负责人，主持1项国家自然基金青年基金和2项面上项目，1项教育部博士点基金和2项重庆市自然基金。

数学与统计学院

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