The Markov Chain Approximation Approach for Numerical Solution of Stochastic Control Problems: Experiences from Merton's Problem

Claus Munk
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Claus Munk: Odense University, Denmark

Finance from EconWPA

Abstract: Many problems in modern financial economics involve the solution of continuous-time, continuous-state stochastic control problems. Since explicit solutions of such problems are extremely rare, efficient numerical methods are called for. The Markov chain approximation approach provides a class of methods that are simple to understand and implement. In this paper, we compare the performance of different variations of the approach on a problem with a well-known solution, namely Merton's consumption/portfolio problem. We suggest a variant of the method, which outperforms the known variants, at least when applied to this specific problem. We document that the size of the contraction parameter of the control problem is of great importance for the accuracy of the numerical results. We also demonstrate that the Richardson extrapolation technique can improce accuracy significantly.

Keywords: Stochastic control; efficient numerical solution; Merton's consumption/portfolio problem (search for similar items in EconPapers)
JEL-codes: C61 G11 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-fmk
Date: 1998-02-11
Note: Type of Document - Latex 2e; prepared on PC; to print on PostScript; pages: 31 ; figures: included
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Persistent link: http://EconPapers.repec.org/RePEc:wpa:wuwpfi:9802002

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