The Markov chain approximation approach for numerical solution of stochastic control problems: Experiences from Merton's problem

Applied Mathematics and Computation

Volumn 136, Issue 1, 2003, Pages 47-77

  Munk, Claus ^a  

^a UNIVERSITY OF SOUTHERN DENMARK   (Denmark)

Author keywords

Consumption and portfolio choice; Convergence of numerical solution schemes; Markov chain approximation; Stochastic optimal control

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; EXTRAPOLATION; MARKOV PROCESSES;

MARKOV CHAIN APPROXIMATION;

STOCHASTIC CONTROL SYSTEMS;

EID: 0037465591     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(02)00016-4     Document Type: Article

References (19)

1. Buchanan J.L., Turner P.R. Numerical Methods and Analysis. 1992;McGraw-Hill, New York.
2. Bunch D., Johnson H. A simple and numerically efficient valuation method for American puts using a modified Geske-Johnson approach. J. Finance. 47:1992;809-816.
3. Christiansen E., Petersen H.G. Estimation of convergence orders in repeated Richardson extrapolation. BIT. 29:1989;48-59.
4. Duffie D. Dynamic Asset Pricing Theory. second ed. 1996;Princeton University Press, Princeton, NJ.
5. Fitzpatrick B.G., Fleming W.H. Numerical methods for an optimal investment-consumption model. Math. Oper. Res. 16(4):1991;823-841.
6. Fleming W.H., Soner H.M. Controlled Markov Processes and Viscosity Solutions. Applications of Mathematics. vol. 25:1993;Springer, New York.
7. Geske R., Johnson H.E. The American put valued analytically. J. Finance. 39(5):1984;1511-1524.
8. Karatzas I., Lehoczky J.P., Sethi S.P., Shreve S.E. Explicit solution of a general consumption/investment problem. Math. Oper. Res. 11(2):1986;261-294.
9. Kushner H.J. Probability Methods for Approximations in Stochastic Control and for Elliptic Equations. Mathematics in Science and Engineering. vol. 129:1977;Academic Press, New York.
10. Kushner H.J. Numerical methods for stochastic control problems in continuous time. SIAM J. Control Optim. 28(5):1990;999-1048.
11. Kushner H.J., Dupuis P.G. Numerical Methods for Stochastic Control Problems in Continuous Time. Applications of Mathematics. vol. 24:1992;Springer, New York.
12. Merton R.C. Lifetime portfolio selection under uncertainty: The continuous-time case. Rev. Econom. Statist. 51:1969;247-257. (Reprinted as Chapter 4 in Merton [15] ).
13. Merton R.C. Optimum consumption and portfolio rules in a continuous-time model. J. Econom. Theory. 3:1971;373-413. (Erratum: Merton [14]. Reprinted as Chapter 5 in Merton [15]).
14. Merton R.C. Erratum. J. Econom. Theory. 6:1973;213-214.
15. Merton R.C. Continuous-time finance. 1992;Basil Blackwell Inc, Padstow, UK.
16. C. Munk, Numerical methods for continuous-time, continuous-state stochastic control problems, Publications from Department of Management 97/11, Odense University, 1997a.
17. C. Munk, Optimal Consumption-Portfolio Policies and Contingent Claims Pricing and Hedging in Incomplete Markets, Ph.D. thesis, Odense University, DK-5230 Odense M, Denmark, 1997b.
18. Rust J. Numerical dynamic programming in economics. Amman H.M., Kendrick D.A., Rust J. Handbook of Computational Economics. vol. I:1996;North-Holland, Amsterdam.
19. Tapiero C.S., Sulem A. Computational aspects in applied stochastic control. Comput. Econom. 7:1994;109-146.