勷勤数学•专家报告

题      目：Asymptotic Results of Tail Moment and Tail Central Moment for Dependent Risks

报  告  人：李津竹   教授  (邀请人：杨舟 )

                                     南开大学

时      间：5月29日  16：00-17：00

地     点：数科院西楼二楼会议室

报告人简介:

       李津竹，南开大学数学科学学院教授，博士生导师，主要从事随机过程及其在金融保险中的应用研究，目前主持国家自然科学基金面上项目1项，参与国家自然科学基金重点项目1项，在《Adv. in Appl. Probab.》、《Bernoulli》、《Insurance Math. Econom.》、《Scand. Actuar. J.》、《Astin Bull.》等主流期刊发表学术论文30余篇。

摘      要：

       Consider a financial or insurance system with a finite number of individual risks described by real-valued random variables. We focus on two kinds of risk measures, referred to as the tail moment (TM) and tail central moment (TCM), which are defined as the conditional moment and conditional central moment of some individual risk in the event of system crisis. Asymptotic expressions are derived for the TM and TCM with any positive integer orders, when the individual risks are pairwise asymptotically independent and have the distributions from certain classes including both light-tailed and heavy-tailed distributions. The obtained formulas possess concise forms unrelated to dependence structures, and hence enable us to estimate the TM and TCM efficiently. Some issues about premium principle and optimal capital allocation are revisited in the asymptotic point of view to demonstrate wide applications of our results. We also give a numerical study on the relative errors of the obtained asymptotic results under some specific scenarios when there are two individual risks in the system. The corresponding asymptotic properties of the degenerate univariate versions of the TM and TCM will be especially discussed at the end of the talk.

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