报告人：梁歌春教授

时  间：2025年11月25星期二 13:00 -14:00

地  点：腾讯会议：940-2668-5088

报告摘要:

We extend the notion of forward performance criteria to settings with random endowment in incomplete markets. Building on these results, we introduce and develop the novel concept of forward optimized certainty equivalent (forward OCE), which provides a genuinely dynamic valuation mechanism accommodating progressively adaptive market model updates, stochastic risk preferences, and incoming claims with arbitrary maturities.

In parallel, we propose a new methodology for analyzing the resulting stochastic optimization problems by directly studying the candidate optimal control processes for both the primal and dual formulations. Specifically, we derive two new systems of forward-backward stochastic differential equations (FBSDEs) and establish necessary and sufficient optimality conditions, as well as various equivalences between the primal and dual problems.

This approach is general and complements the existing framework for forward performance criteria with random endowment that is based on backward stochastic partial differential equations (backward SPDEs) for the associated value functions. We also present representative examples for both forward performance criteria with random endowment and forward OCE. Furthermore, in the case of exponential criteria, we explore the connection between forward OCE and forward entropic risk measures.

Joint work with Thaleia Zariphopoulou and Yifan Sun.

个人简介:

梁歌春博士是英国华威大学统计系的Reader。他过去的职位包括华威大学副教授、伦敦国王学院讲师和Oxford-Man量化金融研究所博士后研究员。2018-2019年荣获德国弗莱堡大学弗莱堡高等研究院（FRIAS）高级研究员和玛利-居里研究员的称号。2011年获得牛津大学数学研究所数学博士学位。他的研究兴趣主要集中在金融数学和随机分析与控制，并在Annals of Probability、SIAM Journal on Control and Optimization、Journal of Differential Equations, Finance and Stochastics、Mathematical Finance和SIAM Journal on Financial Mathematics等国际期刊发表论文。