大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

Relative wealth concerns with partial information and heterogeneous priors

Chao Zhou (National University of Singapore)

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大阪大学 数理・データ科学セミナー 金融・保険セミナーシリーズ 第117回

Relative wealth concerns with partial information and heterogeneous priors

Chao Zhou (National University of Singapore)

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.