Dynamic portfolio selection under generalized disappointment aversion

This paper addresses the continuous-time portfolio selection problem under generalized disappointment aversion (GDA). The implicit definition of the certainty equivalent within GDA preferences introduces time inconsistency to this problem. We provide the sufficient and necessary conditions for a strategy to be an equilibrium by a fully nonlinear ordinary differential equation (ODE). Through an exploration of the existence and uniqueness of solution to the ODE, we establish the existence and uniqueness of the equilibrium. Our findings indicate that under disappointment aversion (DA) preferences, non-participation in the stock market is the unique equilibrium. The numerical analysis reveals that, under GDA preferences, the investment proportion in the stock market consistently remains smaller than the investment proportion under the classical Expected Utility (EU) theory.