Financial equilibrium with preference updating

Financial equilibrium models provide important information on the movement of asset prices in response to subjective beliefs and consumption patterns of economic agents. It is standard to assume that agents are rational and have fixed preferences from the outset—in particular, these do not depend on other agents’ actions in the market. This work deviates from this assumption by allowing the subjective views and consumption clocks of an individual agent to depend on the whole history of the wealth and consumption distribution across agents in the economy. The updating mechanism is generic and may accommodate different behavioural models; for example, it can model herding. In order to analyse existence and uniqueness of equilibrium, we assume that agents have numeraire-invariant preferences, which are rich enough to render any observe agents’ behaviour optimal. The market contains a borrowing and lending account in zero net supply, as well as a stock in positive net supply providing certain dividend stream, exogenously specified. A characterisation of existence and uniqueness of equilibrium in a Brownian setting is provided in terms of stochastic differential equations. The proposed framework naturally allows for equilibria where the risky asset in positive net supply is suboptimal to hold for investment.