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Optimal Consumption with Loss Aversion and Reference to Past Spending Maximum

Abstract 

This talk studies an optimal consumption problem for a loss-averse agent with reference to past consumption maximum. To account for loss aversion on relative consumption, an S-shaped utility is adopted that measures the difference between the non-negative consumption rate and a fraction of the historical spending peak. We consider the concave envelope of the realization utility with respect to consumption, allowing us to focus on an auxiliary HJB variational inequality on the strength of concavification principle and dynamic programming arguments. By applying the dual transform and smooth-fit conditions, the auxiliary HJB variational inequality is solved in closed-form piecewisely and some thresholds of the wealth variable are obtained. The optimal consumption and investment control of the original problem can be derived analytically in the piecewise feedback form. The rigorous verification proofs on optimality and concavification principle are provided. Joint with Prof. Xiang YU and Mr. Qinyi Zhang.


报告人简介:李迅,香港理工大学应用数学系教授(tenure),2000 年在香港中文大学系统工程和工程管理系获博士学位。2000 年-2001 年在香港中文大学系统工程和工程管理系开展博士后研究。2001 年-2003 年在卡尔加里大学数学和计算金融实验室开展博士后研究。2003 年-2007 年在新加坡国立大学数学系任 Visiting Fellow 。2007 年加入香港理工大学应用数学系,现为该系终身教职教授。主要研究兴趣为应用概率、随机控制论及其金融应用。其论文主要发表在 SIAM Journal on Control and Optimization, Annals of Applied Probability, IEEE Transactions on Automatic Control, Automatica, Mathematical Finance and Quantitative Finance 等国际著名期刊 ,共计70 余篇。