Stochastics and Finance: Chao Zhou -- Relative wealth concerns with partial information and heterogeneous priors

Dear All, 

 You are kindly invited to attend the next Stochastics and Finance seminar.  On Tuesday
October 20 at 3pm (Sydney time) Chao Zhou will give a talk via Zoom.  

Zoom link: https://uni-sydney.zoom.us/j/94360647811 

Speaker: Dr Chao Zhou (National University of Singapore) 

Title: Relative wealth concerns with partial information and heterogeneous priors 

Abstract: We establish a Nash equilibrium in a market with N agents with CARA utility
and the relative performance criteria when the market return is unobservable.  Each
investor has a Gaussian prior belief on the return rate of the risky asset.  The
investors can be heterogeneous in both the mean and variance of the normal random
variable.  By a separation result and a martingale argument, we show that the optimal
investment strategy under a stochastic return rate model can be characterized by a
fully-coupled FBSDE with linear coefficients.  Two sets of deep neural networks are used
for the numerical computation to first find each investor’s estimate of the mean
return rate and then solve the FBSDEs.  We are the first to establish the uniqueness
result for the class of FBSDEs with stochastic coefficients.  The deep learning scheme
for solving the game under partial information is also novel.  We demonstrate the
efficiency and accuracy by comparing with the numerical solution from PDE for the linear
filter case and apply the algorithm to the general case of nonlinear hidden variable
process.  Simulations of investment strategies demonstrate a herd effect that investors
trade more aggressively under relative performance, in most cases for our specified
market parameters.  Statistical properties of the investment strategies and the
portfolio performance, including the Sharpe ratios and VRRs are examed.  This is a joint
work with Chao DENG and Xizhi SU.  



http://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