Equilibrium Multi-Agent Model With Heterogeneous Views on Fundamental Risks

Abstract

This article presents an equilibrium-based multi-agent optimal consumption and portfolio problem incorporating sentiments, where multiple agents have heterogeneous (optimistic, pessimistic, neutral) views on fundamental risks represented by Brownian motions. Each agent maximizes its expected utility on consumption under its subjective probability measure, reflecting its heterogeneous views on fundamental risks. Specifically, we formulate the individual optimization problem as an optimal consumption and portfolio problem with a choice of a probability measure, which we solve by a Malliavin calculus approach. Moreover, we provide the state-price density process in a market equilibrium that includes information on the interest rate and the market price of risk. Finally, we present numerical examples on an interest rate model, which show how the multiple agents' views on the fundamental risks affect the yield curve shapes.