Multi-agent equilibrium model with heterogeneous views on fundamental risks in incomplete market

Abstract

This paper considers a multi-agent optimal investment problem with conservative, aggressive, or neutral views in an incomplete market by a backward stochastic differential equation (BSDE) approach. In particular, we formulate the conservative, aggressive, and neutral views of the agents through a sup-inf/inf-sup, sup-sup, or sup problem where the infimum or supremum is taken over a choice of a probability measure depending on the view types and the supremum is taken over trading strategies. To the best of our knowledge, this is the first attempt to investigate a multi-agent equilibrium, namely, an equilibrium of demand and supply in a market with multiple agents in an incomplete setting with heterogeneous views on Brownian motions. Moreover, we present a square-root case where agents have conservative, aggressive, or neutral views on the fundamental risks and a general case in which the Sharpe ratio process of the risky asset and the optimal trading strategies in equilibrium are explicitly solved using a BSDE approach. Finally, we present numerical examples of the trading strategies and the expected return process in equilibrium under heterogeneous views, illustrating how the conservative, aggressive, or neutral views affect the Sharpe ratio process of the risky asset and the trading strategies of the agents in equilibrium.