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284期讲座

(2026年4月24日)

讲座主题1：Optimal portfolio choice with comfortable consumption

摘要：In this talk we investigate a Merton-type portfolio optimization problem with a minimum comfortable consumption constraint, utilizing a stochastic control approach. By translating the HJB equations into second-order ordinary differential equations through a novel method, we precisely characterize the set of candidate value functions. We then identify the optimal consumption rate, investment strategy and the value function explicitly by extending the recent stochastic perturbation method presented in Herdegen, Hobson and Jerome (2021). This approach can be applied to derive explicit solutions for other portfolio choice problems under constraints, with detailed studies of the corresponding HJB equations. In addition, we have extended the model when inflation is considered. We also discuss some applications, such as retirement funds, pension funds, endowment portfolios and the AK model for economic growth.

报告人：田德建

嘉宾简介：田德建，中国矿业大学数学学院副教授。主要研究领域：随机分析与金融数学，聚焦BSDE理论及其在金融中的应用，金融风险度量和投资组合优化等方向。在Finance and Stochastics、SIAM Journal on Financial Mathematics、Stochastic Processes and their Applications、Quantitative Finance等金融数学和应用概率论学术刊物上发表（含接收）论文30余篇。主持完成国家自然科学基金青年基金项目一项。

讲座主题2：Insurance demand under government interventions and distorted probabilities

摘要：In this talk, we investigate the optimal insurance demand for an individual under distorted probabilities, considering the participation of government interventions, such as premium subsidies and disaster relief. We model the premium subsidy as a non-decreasing function ranging from 0 to 1, representing the percentage of government support, whereas the relief assistance is characterized by a 1-Lipschitz relief scheme function, reflecting the government's effort in post-disaster recovery. When the expected-value premium principle is employed, the general form of the optimal retained loss function for the policyholder is derived under a concave government relief scheme. We demonstrate that the optimal retained loss function takes a layered form, shaped by the trade-off between government premium subsidies and relief assistance, and can be further characterized by an ordinary integrodifferential equation. In particular, explicit solutions are obtained for VaR and general convex distortion risk measures. To provide further insights, we explore two extensions: one investigates the design of the optimal safety loading from the insurer's perspective, while the other examines the impact of the government's budget constraint. Finally, we present numerical examples to illustrate and validate the main theoretical findings.

报告人：张艺赢

嘉宾简介：张艺赢，南方科技大学数学系副研究员、助理教授、博士生导师。2018年9月博士毕业于香港大学统计与精算学系，随后赴鲁汶大学和阿姆斯特丹大学进行联合学术访问。2019.1-2021.8在南开大学统计与数据科学学院工作，任助理教授，2021年8月加入南方科技大学数学系，任助理教授。主要研究兴趣包括最优保险设计、巨灾保险、风险减量、风险度量、信度理论、系统性风险等。研究成果主要发表在保险精算、金融数学、经济学和运筹管理等领域主流期刊，如：IME、ASTIN Bulletin、SAJ、NAAJ、SIFIN、QF、JEDC、EJOR、RESS、NRL等杂志。正在主持国自然面上1项、深圳市面上2项，主持完成国自然青年等项目3项。

讲座主题3：Technology and insurance for climate risk management under uncertainty

摘要：This talk investigates the optimal timing for a firm to invest in green technology to mitigate the adverse effects of climate change on its consumption, while incorporating insurance to transfer climate-related risks. The firm faces uncertainties in the probability of catastrophic events, which cannot be directly observed. This incomplete information adds a layer of complexity to the decision-making process. We adopt a Bayesian learning approach to model uncertainty through a posterior belief process, with the objective of maximizing the firm's expected consumption by determining the optimal investment threshold. In high-dimensional settings, the classical smooth-fit condition may fail, rendering standard optimal stopping methods inadequate. To address this, we employ state-space transformations and probabilistic techniques to handle irregularities in the value function and the structure of the free boundary. Our framework enhances the tractability and flexibility of solving complex optimal control problems under uncertainty. A numerical example illustrates how key parameters influence the optimal investment boundary.

报告人：张建楠

嘉宾简介：张建楠，现任对外经济贸易大学保险学院统计与精算系讲师。她于2022年获得墨尔本大学精算学博士学位，曾在新南威尔士大学担任博后研究员。当前研究方向主要为随机控制在金融与保险领域的应用，涵盖气候风险、网络风险及契约理论等方向。目前在精算学、应用数学等领域知名期刊Insurance: Mathematics and Economics、Scandinavian Actuarial Journal、Journal of Mathematical Analysis and Applications、Applied Mathematics and Computation等发表论文十余篇。

讲座时间：2026年4月24日（周五） 上午8:30-12:00

报告地点：学院南路校区学术会堂602

邀 请 人：池义春