The Markov chain approximation approach for numerical solution of stochastic control problems: experiences from Merton's problem.
type: Item
instance of: scholarly article
title: The Markov chain approximation approach for numerical solution of stochastic control problems: experiences from Merton's problem.
zbMATH Open document ID: 1052.93061
DOI: 10.1016/S0096-3003(02)00016-4
author: Claus Munk
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: It is well known that many problems of financial economics lead to the solutions of continuous-time, continuous-state stochastic control problems. Since to solve such problems exactly is very complicated, approximative methods have to be mostly employed. The diffusion continuous-time, continuous-state process is then replaced by a discrete-time, discrete-state Markov chain and, consequently, the original problem is (by this approach) replaced by a Markov chain control problem. The aim of this publication is to compare various versions of the Markov chain approximation approach in the case of Merton's simple consumption/investment problem for which an explicit solution is known. It follows from the paper that the above mentioned approximations are suitable. Of course, the behaviour of the approximation depends on the determination of an upper bound on the state space for the approximating Markov chain (namely the original process is unbounded). Moreover, it follows from the paper that the Richardson extrapolation technique can be successively employed to improve the solution.
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 91B42
Mathematics Subject Classification ID: 91G10
Mathematics Subject Classification ID: 65C40
Mathematics Subject Classification ID: 60J22
zbMATH DE Number: 1861371
zbMATH Keywords: Markov chain approximation
zbMATH Keywords: Merton's consumption/investment problem
zbMATH Keywords: Richardson extrapolation
reviewed by: Vlasta Kaňková
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1861371