勷勤数学•专家报告

题      目：Monotone mean-variance investment-reinsurance under the Cramer-Lundberg model

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： 1月10日  10：00-11:00

地     点：数科院东楼401

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 an optimal investment-reinsurance problem for an insurer (she) under the Cramer-Lundberg model with monotone mean-variance (MMV) criterion. At any time, the insurer can purchase reinsurance or acquire new business and invest in a security market consisting of a risk-free asset and multiple risky assets whose excess return rate and volatility rate are allowed to be random. The trading strategy is subject to a general convex cone constraint, encompassing no-shorting constraint as a special case. The optimal investment-reinsurance strategy and optimal value for the MMV problem are deduced by solving certain backward stochastic differential equations with jumps. In the literature, it is known that models with MMV criterion and mean-variance criterion lead to the same optimal strategy and optimal value when the wealth process is continuous. Our result shows that the conclusion remains true even if the wealth process has compensated Poisson jumps and the market coefficients are random.

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