The Markov Chain Approximation Approach for Numerical Solution of Stochastic Control Problems: Experiences from Merton's Problem
AbstractMany 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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Bibliographic InfoPaper provided by EconWPA in its series Finance with number 9802002.
Length: 31 pages
Date of creation: 11 Feb 1998
Date of revision:
Note: Type of Document - Latex 2e; prepared on PC; to print on PostScript; pages: 31 ; figures: included
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Stochastic control; efficient numerical solution; Merton's consumption/portfolio problem;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
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- R. C. Merton, 1970.
"Optimum Consumption and Portfolio Rules in a Continuous-time Model,"
58, Massachusetts Institute of Technology (MIT), Department of Economics.
- 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.
- 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.
- 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.
- Simon Lysbjerg Hansen, 2005. "A Malliavin-based Monte-Carlo Approach for Numerical Solution of Stochastic Control Problems: Experiences from Merton's Problem," Computing in Economics and Finance 2005 391, Society for Computational Economics.
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