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

  • Claus Munk

    (Odense University, Denmark)

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.

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File URL: http://128.118.178.162/eps/fin/papers/9802/9802002.pdf
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Paper provided by EconWPA in its series Finance with number 9802002.

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Length: 31 pages
Date of creation: 11 Feb 1998
Date of revision:
Handle: RePEc:wpa:wuwpfi:9802002
Note: Type of Document - Latex 2e; prepared on PC; to print on PostScript; pages: 31 ; figures: included
Contact details of provider: Web page: http://128.118.178.162

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  1. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
  2. Rust, John, 1996. "Numerical dynamic programming in economics," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 14, pages 619-729 Elsevier.
  3. Bunch, David S & Johnson, Herb, 1992. " A Simple and Numerically Efficient Valuation Method for American Puts Using a Modified Geske-Johnson Approach," Journal of Finance, American Finance Association, vol. 47(2), pages 809-16, June.
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