勷勤数学•专家报告
题 目：Stochastic Stackelberg differential investment and reinsurance game with ambiguous correlation.
报 告 人： 彭幸春 副教授 (邀请人：杨舟)
武汉理工大学
时 间： 11月10日 10：00-11:00
地 点：数科院东楼401
报告人简介:
彭幸春，武汉理工大学数学与统计学院副教授，一直从事保险精算和金融数学的相关研究，主要研究保险和金融中的随机控制与优化问题。以第一作者或通讯作者身份在 Insurance: Mathematics and Economics, Annals of Operations Research, Scandinavian Actuarial Journal, Physica D: Nonlinear Phenomena, Journal of Computational and Applied Mathematics等权威期刊发表高水平论文30余篇。主要学术兼职包括中国现场统计研究会风险管理与精算分会理事、中国现场统计研究会多元分析应用专业委员会理事、全国工业统计学教学研究会数字经济与区块链协会理事、中国工业与应用数学学会精算与保险青年专业委员会委员等等。
摘 要：
This paper investigates a Stackelberg investment and reinsurance game with the ambiguous correlation between the financial and insurance markets. The ambiguous correlation is modeled by constructing a set of non-equivalent prior probability measures under the G-framework. The reinsurer acts as the leader charging reinsurance premiums, while the insurer acts as the follower participating in proportional reinsurance. Both the reinsurer and the insurer invest in the financial market with the aim to maximize the expected utility of their terminal wealth under the worst-case scenario. Based on the dynamic programming principle under G-Brownian motion, the Stackelberg equilibrium strategies are derived by solving the Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations. Through theoretical analysis and numerical simulation, the influence of ambiguity on the Stackelberg equilibrium strategies is analyzed. We find that both the insurer and reinsurer adopt more conservative strategies in the presence of market correlation ambiguity, with the insurer being more significantly affected by such ambiguity, while the reinsurer is less influenced. When both the insurer and the reinsurer maintain investment in the risky asset, the ambiguity faced by the insurer leads to higher reinsurance premiums, whereas the ambiguity faced by the reinsurer results in lower reinsurance premiums.
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