Equilibrium portfolio selection under beliefs-dependent utilities

TL;DR

This paper develops a framework for equilibrium portfolio selection in a regime-switching market with beliefs-dependent utilities, deriving explicit solutions and analyzing how market regimes influence optimal strategies.

Contribution

It introduces a novel equilibrium approach for beliefs-dependent utilities in regime-switching markets, including closed-form solutions and rigorous verification.

Findings

Equilibrium strategies vary between bull and bear regimes.

Optimal risky asset allocation is higher in bull markets.

Portfolio proportions change over time depending on market regime.

Abstract

This paper investigates portfolio selection within a continuous-time financial market with regime-switching and beliefs-dependent utilities. The market coefficients and the investor's utility function both depend on the market regime, which is modeled by an observable finite-state continuous-time Markov chain. The optimization problem is formulated by aggregating expected certainty equivalents under different regimes, leading to time-inconsistency. Utilizing the equilibrium strategy, we derive the associated extended Hamilton-Jacobi-Bellman (HJB) equations and establish a rigorous verification theorem. As a special case, we analyze equilibrium portfolio selection in a beliefs-dependent risk aversion model. In a bull regime, the excess asset returns, volatility, and risk aversion are all low, while the opposite holds in a bear regime. Closed-form solutions in the CRRA preference regime model of bull and bear markets are obtained, which is expressed by a solution to four-dimensional non-linear ODEs. The global existence of the ODEs is proven and we verify the equilibrium solution rigorously. We show that the equilibrium investment strategy lies between two constant Merton's fractions. Additionally, in our numerical experiment, the equilibrium proportion allocated in the risky asset is greater in a bull regime than in a bear regime and the equilibrium proportion increases with time in a bull regime while decreasing in a bear regime.