Dynamic Money Doctors under Cumulative Prospect Theory

Abstract

We investigate the interaction between investors and portfolio managers under cumulative prospect theory. We model trust in the manager and the relative anxiety about investing in a risky asset in an original way. Moreover, we study how trust and anxiety affect the manager’s fee and the portfolios of cumulative prospect theory investors. In contrast to previous work using the classical mean-variance preferences, there are two main novelties in our contribution. First, our research relies on cumulative prospect theory (CPT) rather than the classical mean-variance framework. Second, we focus on a dynamic portfolio selection. In other words, we formulate the optimal problem under multi-period setting. Besides, we attain an optimal portfolio choices in multi-period relying on the sub-game perfect investment strategies. Moreover, our research differs from traditional CPT work through an improved value function that accurately characterizes the reduction in anxiety suffered by the CPT investors from bearing risk when assisted by the portfolio managers’ help relative to when they lack such assistance.