Dear All, You are kindly invited to attend the next Stochastics and Finance seminar. On Wednesday April 14 at 2pm (Sydney time) Xiang Yu will give a talk via Zoom. Zoom link: https://uni-sydney.zoom.us/j/87491585109 Speaker: Dr Xiang Yu (Hong Kong Polytechnic University) Title: Optimal consumption with reference to past spending maximum: exponential utility and S-shaped utility cases Abstract: In this talk, we present two recent studies on the optimal consumption with the non-negativity constraint and the path-dependent reference to the past consumption peak under the exponential utility and the S-shaped utility. In both problems, the relative performance is measured by the distance between the current consumption rate and a fraction of the historical consumption maximum. The reference process is non-addictive in the sense that the investor is allowed to strategically consume below the reference level. By applying the dynamic programming argument and identifying the value function depending on the wealth variable and the reference variable, we can express the associated HJB equation in the piecewise manner across difference regions together with some free boundary conditions. In both problems, the thresholds for the wealth level can be characterized by nonlinear functions of the reference variable such that the optimal consumption in each region can be obtained in the feedback form that satisfies: (i) zero consumption; (ii) consumption below the reference; (iii) consumption above the reference but below the historical maximum; (iv) consumption sitting at the previous historical maximum; (v) consumption creating a new global maximum. Distinct optimal consumption behavior and financial implications will be concluded under two types of utility functions, and some comparison results with respect to loss aversion on the relative consumption will be provided. https://www.maths.usyd.edu.au/u/SemConf/Stochastics_Finance/seminar.html Please feel free to forward this message to anyone who might be interested in this talk. Kind regards, Anna