Multi-agent Robust Optimal Investment Problem in Incomplete Market

Abstract

This paper considers a multi-agent optimal investment problem with conservative sentiments in an incomplete market by a BSDE approach. Particularly, we formulate the conservative sentiments of the agents by a sup-inf/inf-sup problem where we take infimum on a choice of a probability measure 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 and a general case where the trading strategies and the excess return process of the risky asset in equilibrium are explicitly solved. Finally, we present numerical examples of the trading strategies and the expected return process in equilibrium under conservative sentiments, which explain how the sentiments affect the trading strategies of the agents and the expected return process of the risky asset.