报告人：吴臻教授 

               山东大学

题目: Optimal Switching Problem with Two-Time-Scale Markov Chains: BSDEs，HJB equation and Stock Trading

时间：2019年01月11日下午17:00

地点：海韵行政楼B313

摘要: This talk is concerned with backward stochastic differential equations (BSDEs) and optimal switching problem coupled by  continuous-time finite-state Markov chain which has a two-time-scale structure, i.e., the states of the Markov chain can be divided into a number of groups such that the chain jumps rapidly within a group and slowly between the groups. In this talk, we give some convergence results as the fast jump rate goes to infinity, which can be used to reduce the complexity of the original problem. This method is also referred to as singular perturbation. The first result is the weak convergence of the BSDEs with two-time-scale Markov chains. It is shown that the solution of the original BSDE system converges weakly under the Meyer-Zheng topology to that of an aggregated BSDE system. Then we focus on the optimal switching problem for regime switching model with two-time-scale Markov chains. We obtain the optimal switching strategy by virtue of dynamic programming principle and related HJB equation—a system of variational  inequality，and prove the convergence of the value function under the two-time-scale structure. Finally, as an  application of the theoretical results, an example concerning the stock trading problem in a regime switching market is provided. Both the optimal trading rule and convergence result are numerically demonstrated in this example. 

报告人简介：吴臻老师是山东大学数学学院教授、博士生导师，享受国务院政府特殊津贴，研究领域涉及概率论、控制论、微分对策和金融数学等，特别是在正倒向随机微分方程与随机最优控制理论及其在金融中的应用方面取得突出的研究成果，得到国内外同行的高度认可。吴臻教授2011年获批国家杰出青年科学基金，2013年作为“金融数学”重点领域创新团队负责人入选科技部首批国家创新人才推进计划；2014年入选国家“特支”首批科技创新领军人才；2015年受聘为教育部国家级高层次人才，获得“国家有突出贡献中青年专家”荣誉称号。吴臻教授在教学上也取得丰硕成果，是山东省优秀研究生指导教师，主持国家精品课程，曾3次获得国家教学成果二等奖。吴臻教授现任国际控制理论权威期刊SIAM Journal on Control and Optimization（SIAM控制与优化杂志）和SCI学术期刊Statistics & Probability Letters（统计与概率通讯）编委、国家自然科学基金数学天元基金学术领导小组成员、中国数学会理事、中国自动化学会控制理论专业委员会委员、山东数学会理事长，并且是被山东省人民政府金融工作办公室咨询专家。

联系人：刘继春教授

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