Behavioral Portfolio Selection in Continuous Time

TL;DR

This paper develops a continuous-time behavioral portfolio model based on prospect theory, addressing issues of ill-posedness, and derives explicit optimal strategies that resemble gambling policies, with applications to CRRA utility.

Contribution

It introduces a systematic method to solve well-posed behavioral portfolio models with prospect theory, providing explicit solutions and insights into risky asset allocations.

Findings

Explicit optimal terminal wealth structures resemble gambling policies.

Identifies classes of ill-posed models and proposes solutions for well-posed cases.

Demonstrates the model with a complete solution for two-piece CRRA utility.

Abstract

This paper formulates and studies a general continuous-time behavioral portfolio selection model under Kahneman and Tversky's (cumulative) prospect theory, featuring S-shaped utility (value) functions and probability distortions. Unlike the conventional expected utility maximization model, such a behavioral model could be easily mis-formulated (a.k.a. ill-posed) if its different components do not coordinate well with each other. Certain classes of an ill-posed model are identified. A systematic approach, which is fundamentally different from the ones employed for the utility model, is developed to solve a well-posed model, assuming a complete market and general It\^o processes for asset prices. The optimal terminal wealth positions, derived in fairly explicit forms, possess surprisingly simple structure reminiscent of a gambling policy betting on a good state of the world while accepting a fixed, known loss in case of a bad one. An example with a two-piece CRRA utility is presented to illustrate the general results obtained, and is solved completely for all admissible parameters. The effect of the behavioral criterion on the risky allocations is finally discussed.