教育部人文社科重点研究基地中央财经大学中国精算研究院学术活动

精算论坛第220期讲座

(2022年12月19日下午2:00-4:00)

讲座主题一：Optimal investment and benefit adjustment problem for a collective DC pension plan with longevity trend under CEV model

摘要： This paper studies the optimal investment and benefit adjustment problem for a collective DC pension plan under longevity trend. We assume that the mortality hazard rate is a function of age and time, which extend the Makeham's Law and can describe the longevity trend. The contribution rate is a predetermined proportion of average salary while the benefit payments depends on the pension wealth. The pension fund is allowed to invest in a risk-free asset and a risky asset whose price process satisfies the CEV model. The objective is expected utility maximization of terminal wealth and cumulative weighted product of benefit and wealth. By applying dynamic programming approach, we establish the corresponding Hamilton-Jacobi-Bellman equation and obtain the optimal investment and benefit strategies for CARA and CRRA utilities, respectively. Finally, numerical example is provided to analyze the effects of parameters on the optimal strategies. The results show that under the CARA utility function, only the optimal benefit strategy is related to longevity trend, while under the CRRA utility function, longevity trend has effects on both the optimal benefit and investment strategies.

报告人：赵慧

天津大学数学学院副教授，现任国际自动控制联合会(The International Federation of Automatic Control)社会科学分组技术委员会委员、天津市工业与应用数学学会理事。作为项目负责人，主持3项国家自然科学基金项目（其中青年项目1项，面上项目2项），主持天津市自然科学基金面上项目1项。在《European Journal of Operational Research》、《Insurance: Mathematics and Economics》、《Quantitative Finance》、《Scandinavian Actuarial Journal》等金融精算领域重要期刊发表论文30余篇。入选天津市131创新型人才培养工程第三层次人选和天津大学北洋青年骨干教师、北洋学者。

讲座主题二：Equilibrium investment strategy with learning about equity return

摘要： This paper investigates a dynamic investment decision problem with mean-variance criterion under partial information, where the stock return is assumed to consist of an observable factor and an unobservable factor, which both follow mean reversion processes. Through the Bayesian learning mechanism, the unobservable components of stock returns can be learned by investors from available information, including stock prices and observable returns. Due to lack of time consistency in dynamic investment decision problem with mean-variance criterion, we solve this problem by using a game theory approach developed in Bjork et al. (2017) and seek the equilibrium investment strategy. Through the extended Hamilton-Jacobi-Bellman equation (HJB) equations system, we obtain the analytic solution of the dynamic mean-variance model. In addition, the influence of unobserved predictor and learning mechanism on the equilibrium investment strategy is also analyzed by utilizing numerical examples.

报告人：李永武

北京工业大学经济与管理学院副教授，硕士生导师。曾先后在中国科学院数学与系统科学研究院、香港理工大学从事博士后研究工作。研究兴趣主要包括金融工程，随机最优控制、机器学习及其在金融中的应用。在金融资产配置与风险管理，最优分红问题，养老基金投资管理以及保险合约设计等方面已在国内外著名期刊《Insurance: Mathematics and Economics》、《Journal of Optimization Theory and Applications》、《IEEE Systems Journal》、《Applied Stochastic Models in Business and Industry》、《Operations Research Letters》、《Financial Innovation》、《系统工程理论与实践》、《管理评论》等发表论文20多篇。已主持完成一项国家自然科学基金青年项目，一项国家博士后科学基金项目。现主持一项北京市自然科学基金面上项目，参与一项国家自然科学基金重点项目。兼任中国管理现代化研究会管理与决策科学专业委员会理事,中国优选法统筹法与经济数学研究会量化金融与保险分会理事，美国《Mathematical Reviews》评论员。

讲座时间：2022年12月19日下午2:00-4:00

报告地点：腾讯会议（会议ID：795-869-729）

邀请人：伍慧玲

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