An elementary approach to the Merton problem

Herdegen, Martin, Hobson, David and Jerome, Joseph ORCID: 0000-0002-8312-0053 (2021) An elementary approach to the Merton problem. MATHEMATICAL FINANCE, 31 (4). pp. 1218-1239.

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Official URL: http://dx.doi.org/10.1111/mafi.12311

Abstract

<jats:title>Abstract</jats:title><jats:p>In this article we consider the infinite‐horizon Merton investment‐consumption problem in a constant‐parameter Black–Scholes–Merton market for an agent with constant relative risk aversion <jats:italic>R</jats:italic>. The classical primal approach is to write down a candidate value function and to use a verification argument to prove that this is the solution to the problem. However, features of the problem take it outside the standard settings of stochastic control, and the existing primal verification proofs rely on parameter restrictions (especially, but not only, <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/mafi12311-math-0001.png" xlink:title="urn:x-wiley:09601627:media:mafi12311:mafi12311-math-0001" />), restrictions on the space of admissible strategies, or intricate approximation arguments. The purpose of this paper is to show that these complications can be overcome using a simple and elegant argument involving a stochastic perturbation of the utility function.</jats:p>

Item Type:	Article
Uncontrolled Keywords:	investment, consumption, Merton problem, primal approach, verification argument
Divisions:	Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	14 Mar 2022 17:10
Last Modified:	04 Sep 2023 02:30
DOI:	10.1111/mafi.12311
Open Access URL:	https://onlinelibrary.wiley.com/doi/10.1111/mafi.1...
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3150774