一、题目
Optimal Consumption with Loss Aversion and Reference to Past Spending Maximum
二、主讲人：
Xun LI
三、摘要
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.
四、主讲人简介
Prof. Xun LI received his Ph.D. degree in 2000 from the Department of Systems Engineering and Engineering Management at the Chinese University of Hong Kong, and he stayed with the same department as a postdoctoral research fellow until 2001. From 2001 to 2003, he was a postdoctoral fellow in the Mathematical and Computational Finance Laboratory at the University of Calgary. From 2003 to 2007, he was a visiting fellow in the Department of Mathematics at the National University of Singapore. He joined the Department of Applied Mathematics at the Hong Kong Polytechnic University as Assistant Professor in 2007, Associate Professor in 2013, and is currently Professor. His main research areas are stochastic control and applied probability with financial applications, and he has published in journals such as SIAM Journal on Control and Optimization, Annals of Applied Probability, IEEE Transactions on Automatic Control, Automatica, Journal of Differential Equations, Mathematical Finance, Finance and Stochastics, and Quantitative Finance.
五、邀请人
聂天洋 数学学院教授
六、时间
6月7日（周二）15:00-16:00
七、地点
腾讯会议
联系人：聂天洋，联系方式：nietianyang@sdu.edu.cn
八、主办方
山东大学数学学院
