勷勤数学•专家报告

题      目：Time-consistent per-loss reinsurance and investment in correlated markets with smooth ambiguity

报  告  人：梁志彬  教授  (邀请人：杨舟)

                                   南京师范大学

时      间：8月15日  10：00-11：00

地     点：数科院401

报告人简介:

       南京师范大学数学科学学院教授，博士生导师。主要研究方向：风险管理与精算，数理金融与定价，随机最优风险控制。目前感兴趣的研究领域是：金融保险市场不确定环境下的博弈与优化；深度学习算法下的量化金融与随机最优控制。近年来，在SAJ，IME，EJOR，AMO等数理金融与精算以及优化相关期刊发表学术论文50余篇，主持和完成国家自然科学基金项目以及省部级基金项目多项。08年以来，先后访问过英国London Imperial College的Tanaka商学院；美国University of Michigan的数学系（先后三年半）；加拿大Concordia University的数学与统计系；美国北卡州立大学数学系；以及多次访问香港大学的统计与精算系等。

摘      要：

       In this paper, we study the time-consistent per-loss reinsurance and investment strategies in corre- lated markets for an insurer to maximize its mean-variance criterion, where the insurance market and financial market are correlated due to the so-called thinning dependence generated from an external stochastic source. We also consider the insurer’s ambiguity towards the external source. Specifically, the intensity of the number of events from the external stochastic source cannot be estimated accurately, and hence is treated as a random variable following the insurer’s prior distribution. We investigate the mean-variance optimization problem under smooth ambiguity, which aims to search the optimal strategies in average case. By solving the extended Hamilton-Jacobi-Bellman(HJB) equations and using the Lagrange multiplier method, we derive the closed-form expressions for the equilibrium reinsurance and investment strategies. The results suggest that reinsurance may take two different forms, and that reinsurance strategies and investment strategies are influenced by each other. Finally, we analyze the property of strategies under one single factor and the interaction between thinning dependence and smooth ambiguity.

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