Relative Wealth Concerns with Partial Information and Heterogeneous Priors

SIAM Journal on Financial Mathematics, Volume 15, Issue 2, Page 360-398, June 2024.
Abstract.We establish a Nash equilibrium for [math] agents with the relative wealth performance criteria when the market return is unobservable. We show that the optimal investment strategy under a stochastic return rate model can be characterized by a fully coupled forward-backward stochastic differential equation (FBSDE). We establish the existence and uniqueness results for the class of FBSDEs with stochastic coefficients and solve the utility game under partial information by using deep neural networks. We demonstrate the efficiency and accuracy by a base-case comparison with the semianalytical solution in the linear case. We examined the Sharpe ratios and the variance risk ratios by numerical simulation. We observe that the agent with the most accurate prior estimate is likely to lead the herd. Moreover, the effect of competition on heterogeneous agents varies more with market characteristics compared to that of the homogeneous case.