南开保险精算大讲堂是南开保险与精算研究院主办的系列讲座，旨在搭建保险精算领域学术交流平台、推动相关领域的研究与合作。讲座主题涵盖保险精算、风险管理、随机过程、大数据等多个领域，欢迎校内外师生积极参加！

本期南开保险精算大讲堂活动安排如下：

讲座题目

基于信念依赖效用的均衡投资组合问题研究

主讲人：关国卉

关国卉，中国人民大学统计学院副教授，应用统计科学研究中心研究员。主要研究领域包括最优再保险，最优资产配置和养老金管理等。在 Mathematics of Operations Research, European Journal of Operational Research, Journal of Economic Dynamics and Co ntrol ， Insurance: Mathematics and Economics 、 Scandinavian Actuar ial Journal 等期刊发表多篇论文，主持国家自科青年项目,国家自科面上项目等。

讲座时间

2025年6月26日（周四）

上午10：00

腾讯会议：735898630

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Abstract:This paper investigates portfolio selection within a continuous-time financial market with regime-switching and beliefs-dependent utilities. The market coefficients and the investor’s utility function both depend on the market regime, which is modeled by an observable finite-state continuous-time Markov chain. The optimization problem is formulated by aggregating expected certainty equivalents under different regimes, leading to time-inconsistency. Utilizing the equilibrium strategy, we derive the associated extended Hamilton-Jacobi-Bellman (HJB) equations and establish a rigorous verification theorem. As a special case, we analyze equilibrium portfolio selection in a beliefs-dependent risk aversion model. In a bull regime, the excess asset returns, volatility, and risk aversion are all low, while the opposite holds in a bear regime. Closed-form solutions in the CRRA preference regime model of bull and bear markets are obtained, which is expressed by a solution to four-dimensional non-linear ODEs. The global existence of the ODEs is proven and we verify the equilibrium solution rigorously. We show that the equilibrium investment strategy lies between two constant Merton’s fractions. Additionally, in our numerical experiment, the equilibrium proportion allocated in the risky asset is greater in a bull regime than in a bear regime and the equilibrium proportion increases with time in a bull regime while decreasing in a bear regime.

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