北大金融数学系-20周年系庆系列报告A-19-Consumption in Incomplete Markets
主 题: 北大金融数学系-20周年系庆系列报告A-19-Consumption in Incomplete Markets
报告人: Gu Wang Assistant Professor (伍斯特理工学院)
时 间: 2017-07-27 15:00-16:00
地 点: 理科1号楼1114
报告人简介：汪谷 Assistant Professor，伍斯特理工学院
于2007年在欧冠联赛直播免费观看取得数学与应用数学学士学位，2013年在波士顿大学取得数学博士学位。在2013年至2015年间，担任密歇根大学博士后助理教授。2015年至今，担任伍斯特理工学院助理教授。研究兴趣包括随机控制，投资与消费最优化策略。文章发表在Finance and Stochastics。担任Mathematics of Operations Research, SIAM Journal on Control and Optimization, Finance and Stochastics等杂志的审稿人。
[报告摘要]: To overcome the intractability of consumption-investment problems in incomplete markets, this paper develops approximate solutions to the maximization of isoelastic utility from consumption with infinite horizon in a market where state variables follow a multivariate diffusion. After proving a general verification theorem that links the solution of the Hamilton-Jacobi-Bellman (HJB) equation to the value function and optimal consumption-investment policies, the paper develops pointwise upper and lower bounds of the value function, which have closed-form solutions in typical models and lead to approximate policies with an explicit bound on the certainty-equivalent loss. These policies are optimal for a fictitious complete market in which the safe rate and state variables follow different dynamics, but excess returns are the same; if the market is complete or utility logarithmic, they are optimal even for the original market. Further, the approximations correspond to sub- and super-solutions to the original HJB equation, and lead to the existence of a solution.
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