报告人：李迅教授（香港理工大学）

时间：2023年3月6日周一下午16：30-17:30

腾讯会议ID：488378701

报告题目：Optimal Consumption with Loss Aversion and Reference to Past Spending Maximum

报告摘要：

    In this talk, we study 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 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 can be derived in the piecewise feedback form. The rigorous verification proofs on optimality and concavification principle are provided. Some numerical sensitivity analysis and financial implications are also presented. This work is to appear in SIAM Journal on Financial Mathematics

报告人简介：

  李迅，香港理工大学应用数学系教授，博导，主要研究领域为随机控制和金融数学。在《SIAM Journal on Control and Optimization》、《Annals of Applied Probability》、《Journal of Differential Equations》、《IEEE Transactions on Automatic Control》、 《Automatica》、 《Mathematical Finance》等国际期刊上发表多篇论文。