学术报告

题      目：Dynamic optimal reinsurance and dividend-payout in a finite time horizon

报  告  人：许左权  教授  (邀请人：杨舟 )

                                    香港理工大学深圳研究院

时      间：3月27日  16：00-17：00

地     点：数科院西楼二楼会议室

报告人简介:

        许左权教授先后于南开大学、北京大学、香港中文大学获得本科、硕士、博士学位，曾任英国牛津大学数学研究所任野村金融数学研究员，并兼任牛津Oxford-Man研究所通讯研究员。现任教于香港理工大学应用数学系，主要从事金融数学理论研究，包括量化行为金融学、投资组合、保险契约理论等研究领域，多次于世界著名学术机构及学术会议上作学术报告，主持过多项国家自然科学基金及香港研究资助局项目。其主要学术成果发表在《Mathematical Finance》,《Anna ls of Applied Probability》，《Finance and Stochastics》，《Mathematics of Operations Research》，《SIAM Journal on Financial Mathematics》，《Quantitative Finance》，《Insurance: Mathematics and Economics》等著名国际学术期刊上。现为著名国际期刊《Mathematics of Operations Research》编委。

摘      要：

        We study a dynamic optimal reinsurance and dividend-payout problem for an insurance company in a finite time horizon. The goal of the company is to maximize the expected cumulative discounted dividend payouts until bankruptcy or maturity which comes earlier. The company is allowed to buy reinsurance contracts dynamically over the whole time horizon to cede its risk exposure with other reinsurance companies. This is a mixed singular-classical control problem and the corresponding Hamilton-Jacobi-Bellman equation is a variational inequality with a fully nonlinear operator and subject to a gradient constraint. We obtain the C2,1 smoothness of the value function and a comparison principle for its gradient function by the penalty approximation method so that one can establish an efficient numerical scheme to compute the value function. We find that the surplus-time space can be divided into three non-overlapping regions by a risk-magnitude and time-dependent reinsurance barrier and a time-dependent dividend-payout barrier. The insurance company should be exposed to a higher risk as its surplus increases; be exposed to the entire risk once its surplus upward crosses the reinsurance barrier; and pay out all its reserves exceeding the dividend-payout barrier. The estimated localities of these regions are also provided. This is a joint work with Guan Chonghu and Zhou Rui.

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