Stochastics and Finance: Xiang Yu -- Optimal consumption with reference to past spending maximum

 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