勷勤数学•专家报告

题      目：Utility maximization in constrained and unbounded financial marketsUtility maximization in constrained and unbounded financial markets: Applications to indifference valuation, regime switching, consumption and Epstein-Zin recursive utility

报  告  人：梁歌春  教授  (邀请人：杨舟)

                                  华威大学

时      间：8月21日  10：30-11：30

地     点：数科院401

报告人简介:

       梁歌春博士是英国华威大学统计系的教授。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。

摘      要：

       This talk presents a systematic study of utility maximization problems for an investor in constrained and unbounded financial markets. Building upon the foundational work of Hu et al. (2005) [Ann. Appl. Probab.15, 1691--1712] in a bounded framework, we extend our analysis to more challenging unbounded cases. Our methodology combines quadratic backward stochastic differential equations with unbounded solutions and convex duality methods. Central to our approach is the verification of the finite entropy condition, which plays a pivotal role in solving the underlying utility maximization problems and establishing the martingale property and convex duality representation of the value processes. Through four distinct applications, we first study utility indifference valuation of financial derivatives with unbounded payoffs, uncovering novel asymptotic behavior as the risk aversion parameter approaches zero or infinity. Furthermore, we study the regime switching market model with unbounded random endowments and consumption-investment problems with unbounded random endowments, both constrained to portfolios chosen from a convex and closed set. Finally, we investigate investment-consumption problems involving an investor with Epstein-Zin recursive utility in an unbounded financial market.

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