勷勤数学•专家报告

题      目：Nonzero-sum Dynkin Games under a Generalised Order Condition: Verification Theorem and Application to Convertible Bonds

报  告  人：梁歌春 教授  (邀请人：杨舟)

                                             英国华威大学

时      间：8月5日  10：30-11：30

地     点：数科院西楼二楼会议室

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：

      We study a two-player nonzero-sum Dynkin game in continuous time, where the payoff functions are not required to satisfy the standard “war of attrition”-type order condition. To address this generalised setting, we establish a verification theorem that yields a system of variational inequalities characterising both the players’ payoffs and their strategies at certain Nash equilibria. As an application, we examine convertible bond problems with tax benefits. In the first example, we demonstrate the existence of multiple nontrivial Nash equilibria. In the second example, we consider the case where a bondholder possesses two units of convertible bonds and may convert them sequentially. This leads to a two-stage nonzero-sum game that also violates the usual order condition. A Nash equilibrium is identified numerically. Joint work with David Hobson and Edward Wang