教育部人文社科重点研究基地永利集团3044中国精算研究院学术活动

精算论坛第278期讲座

(2025年12月24日)

讲座主题（一）：Learning to optimally stop a diffusion process

摘要：We study optimal stopping for diffusion processes with unknown modelprimitiveswithin the continuous-timereinforcement learning (RL) framework developed by Wang et al. (2020), and present applications to option pricing and portfolio choice. By penalizing the correspondingvariationalinequality formulation, we transform the stopping problem into a stochasticoptimal control problem with two actions. We thenrandomisecontrols into Bernoulli distributions and add an entropyregulariserto encourage exploration. We derive a semi-analytical optimal Bernoulli distribution, based on which we devise RL algorithms using the martingale approach established inJiaand Zhou (2022a). We establish a policy improvement theorem and prove the fast convergence of the resulting policy iterations. We demonstrate the effectiveness of the algorithms in pricing finite-horizon American put options, solving Merton's problem with transaction costs, and scaling to high-dimensional optimal stopping problems. In particular, we show that both the offline and online algorithms achieve high accuracy in learning the value functions andcharacterisingtheassociated free boundaries. This is a joint work with Min Dai, Yu Sun, andXunYu Zhou.

报告人：许左权

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》,《Annals 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。

讲座主题（二）：Pareto-optimal reinsurancedesign under worst-case distortion risk measures

摘要：This paper investigates the optimal reinsurance contract problem from the perspective of Pareto optimality, where the insurer and the reinsurer both apply distortion risk measures for reinsurance negotiation. We focus on the case where the risk preferences of both parties are only partially known, and the admissible distortion functions are restricted by elicited preference information such as confidence intervals for the risk of a list of lotteries, as well as possible structural requirements including concavity. Under a general premium principle, we derive analytical forms for the optimal reinsurance indemnity, which only depend on the corresponding worst-case distortion functions from the perspectives of the two negotiating parties. We further show that when only individual-specific preference information is available for both parties, a pair of worst-case distortion functions is step-like and is uniquelydetermined by the associated uncertainty sets. When additional generic information is incorporated, a worst-case distortion function becomes piecewise linear, with parameters that can be computed by solving a constrained finite-dimensional optimization problem. Finally, we illustrate the main findings through numerical examples.

报告人：张艺赢

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、系统性风险等。已发表学术论文约80篇，研究成果主要发表在金融数学、保险精算、经济学和运筹管理等领域主流期刊，如：SIAM Journal on Financial Mathematics、Journal of Economic Dynamics and Control、European Journal of Operational Research、Quantitative Finance、Insurance: Mathematics and Economics、ASTIN Bulletin、Scandinavian Actuarial Journal、North American Actuarial Journal、Naval Research Logistics、TEST、Reliability Engineering & System Safety、Computers & Industrial Engineering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。目前担任国际SCIE期刊《HacettepeJournal of Mathematics and Statistics》编委会成员（统计学Area Editor）。担任中国商业统计学会、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、全国工业统计教学研究会数字经济与区块链技术协会、中国现场统计研究会风险管理与精算分会的理事。

讲座时间：2025年12月24日（周三） 上午9:30-11:30

报告地点：沙河校区学院楼13号215

邀请人：刘敬真