High risk aversion Merton's problem without transversality conditions

TL;DR

This paper solves the high risk aversion Merton problem over an infinite horizon by directly addressing the Hamilton-Jacobi-Bellman equation, avoiding restrictive conditions and transversality constraints, thus establishing existence and optimality of strategies.

Contribution

It introduces a novel approach leveraging homogeneity to solve the HJB equation directly, bypassing traditional restrictive assumptions in high risk aversion portfolio optimization.

Findings

Successfully characterizes optimal strategies without transversality conditions

Provides a new method for handling high risk aversion in infinite horizon problems

Enhances theoretical understanding of portfolio choice under risk aversion

Abstract

This paper revisits the classical Merton portfolio choice problem over infinite horizon for high risk aversion, addressing technical challenges related to establishing the existence and identification of optimal strategies. Traditional methods rely on perturbation arguments and/or impose restrictive conditions, such as large discount rates and/or bounded strategies, to ensure well-posedness. Our approach leverages the problem's homogeneity to directly solve the associated Hamilton-Jacobi-Bellman equation and verify the optimality of candidate strategies without requiring transversality conditions.