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 sentiments in an incomplete market by a BSDE approach. Particularly, we formulate the conservative, aggressive, or neutral sentiments of the agents by a sup-inf/inf-sup, sup-sup, or sup problem where we take infimum or supremum on a choice of a probability measure depending on the view types and supremum on trading strategies. To the best of our knowledge, this is the first attempt to investigate a multi-agent equilibrium model in an incomplete setting with heterogeneous views on Brownian motions. Moreover, we show a square-root case where a group of agents has either conservative, aggressive, or neutral sentiments on the fundamental risks and a general case where the Sharpe ratio process of the risky asset and the optimal trading strategies in equilibrium are explicitly solved by a BSDE approach. Finally, we present numerical examples of the trading strategies and the expected return process in equilibrium under heterogeneous sentiments, which explain how the conservative, aggressive, or neutral sentiments affect the Sharpe ratio process of the risky asset and the trading strategies of the agents in equilibrium.