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An elementary approach to the Merton problem
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Herdegen, Martin, Hobson, David G. and Jerome, Joseph (2021) An elementary approach to the Merton problem. Mathematical Finance, 31 (4). pp. 1218-1239. doi:10.1111/mafi.12311 ISSN 0960-1627.
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Official URL: http://doi.org/10.1111/mafi.12311
Abstract
In this article we consider the infinite-horizon Merton investment-consumption problem in a constant-parameter Black\textendash Scholes\textendash Merton market for an agent with constant relative risk aversion $R$. 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, $R<1$), 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.
| Item Type: | Journal Article | ||||||||
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| Subjects: | H Social Sciences > HB Economic Theory H Social Sciences > HG Finance Q Science > QA Mathematics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
| Library of Congress Subject Headings (LCSH): | Mathematical optimization , Investments -- Decision making -- Statistical methods, Consumption (Economics) , Stochastic control theory | ||||||||
| Journal or Publication Title: | Mathematical Finance | ||||||||
| Publisher: | Wiley-Blackwell Publishing, Inc. | ||||||||
| ISSN: | 0960-1627 | ||||||||
| Official Date: | October 2021 | ||||||||
| Dates: |
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| Volume: | 31 | ||||||||
| Number: | 4 | ||||||||
| Page Range: | pp. 1218-1239 | ||||||||
| DOI: | 10.1111/mafi.12311 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 8 June 2021 | ||||||||
| Date of first compliant Open Access: | 9 June 2021 |
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