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Discretisation of Stochastic Control Problems for Continuous Time Dynamics with Delay

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  • Markus Fischer
  • Markus Reiss

Abstract

As a main step in the numerical solution of control problems in continuous time, the controlled process is approximated by sequences of controlled Markov chains, thus discretizing time and space. A new feature in this context is to allow for delay in the dynamics. The existence of an optimal strategy with respect to the cost functional can be guaranteed in the class of relaxed controls. Weak convergence of the approximating extended Markov chains to the original process together with convergence of the associated optimal strategies is established.

Suggested Citation

  • Markus Fischer & Markus Reiss, 2005. "Discretisation of Stochastic Control Problems for Continuous Time Dynamics with Delay," SFB 649 Discussion Papers SFB649DP2005-038, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Dec 2005.
    • Handle: RePEc:hum:wpaper:sfb649dp2005-038
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2005-038.pdf
    File Function: Revised version, 2005
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    References listed on IDEAS

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    1. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 2005. "Vintage capital and the dynamics of the AK model," Journal of Economic Theory, Elsevier, vol. 120(1), pages 39-72, January.
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    Cited by:

    1. Salvatore Federico, 2011. "A stochastic control problem with delay arising in a pension fund model," Finance and Stochastics, Springer, vol. 15(3), pages 421-459, September.

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    More about this item

    Keywords

    Markov; Markov chain; time dynamics; stochastic control problem;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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