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Volume 3, Issue 1
The State Equations Methods for Stochastic Control Problems

Lijin Wang & Fengshan Bai

DOI: 10.4208/nmtma.2009.m99006

Numer. Math. Theor. Meth. Appl., 3 (2010), pp. 79-96.

Published online: 2010-03

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  • Abstract

The state equations of stochastic control problems, which are controlled stochastic differential equations, are proposed to be discretized by the weak midpoint rule and predictor-corrector methods for the Markov chain approximation approach. Local consistency of the methods are proved. Numerical tests on a simplified Merton's portfolio model show better simulation to feedback control rules by these two methods, as compared with the weak Euler-Maruyama discretisation used by Krawczyk. This suggests a new approach of improving accuracy of approximating Markov chains for stochastic control problems.

  • Keywords

Stochastic optimal control, Markov chain approximation, Euler-Maruyama discretisation, midpoint rule, predictor-corrector methods, portfolio management.

  • AMS Subject Headings

93E20, 93E25, 90C39, 90C40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-3-79, author = {Lijin Wang and Fengshan Bai}, title = {The State Equations Methods for Stochastic Control Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2010}, volume = {3}, number = {1}, pages = {79--96}, abstract = {

The state equations of stochastic control problems, which are controlled stochastic differential equations, are proposed to be discretized by the weak midpoint rule and predictor-corrector methods for the Markov chain approximation approach. Local consistency of the methods are proved. Numerical tests on a simplified Merton's portfolio model show better simulation to feedback control rules by these two methods, as compared with the weak Euler-Maruyama discretisation used by Krawczyk. This suggests a new approach of improving accuracy of approximating Markov chains for stochastic control problems.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2009.m99006}, url = {http://global-sci.org/intro/article_detail/nmtma/5990.html} }
TY - JOUR T1 - The State Equations Methods for Stochastic Control Problems AU - Lijin Wang & Fengshan Bai JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 79 EP - 96 PY - 2010 DA - 2010/03 SN - 3 DO - http://doi.org/10.4208/nmtma.2009.m99006 UR - https://global-sci.org/intro/article_detail/nmtma/5990.html KW - Stochastic optimal control, Markov chain approximation, Euler-Maruyama discretisation, midpoint rule, predictor-corrector methods, portfolio management. AB -

The state equations of stochastic control problems, which are controlled stochastic differential equations, are proposed to be discretized by the weak midpoint rule and predictor-corrector methods for the Markov chain approximation approach. Local consistency of the methods are proved. Numerical tests on a simplified Merton's portfolio model show better simulation to feedback control rules by these two methods, as compared with the weak Euler-Maruyama discretisation used by Krawczyk. This suggests a new approach of improving accuracy of approximating Markov chains for stochastic control problems.

Lijin Wang and Fengshan Bai. (2010). The State Equations Methods for Stochastic Control Problems. Numerical Mathematics: Theory, Methods and Applications. 3 (1). 79-96. doi:10.4208/nmtma.2009.m99006
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