Optimal Portfolio Choice for a Behavioural Investor in Continuous-Time Markets

TL;DR

This paper investigates the optimal investment strategies for a behavioural investor with distorted risk preferences in continuous-time markets, establishing conditions for well-posedness and existence of solutions.

Contribution

It introduces a model combining probability distortion and S-shaped utility for continuous-time portfolio optimization, providing new theoretical conditions for optimal strategies.

Findings

Derived necessary and sufficient conditions for well-posedness.

Proved existence of optimal strategies under verifiable conditions.

Extended classical models to incorporate behavioural risk preferences.

Abstract

The aim of this work consists in the study of the optimal investment strategy for a behavioural investor, whose preference towards risk is described by both a probability distortion and an S-shaped utility function. Within a continuous-time financial market framework and assuming that asset prices are modelled by semimartingales, we derive sufficient and necessary conditions for the well-posedness of the optimisation problem in the case of piecewise-power probability distortion and utility functions. Finally, under straightforwardly verifiable conditions, we further demonstrate the existence of an optimal strategy.