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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.

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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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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2005-038.

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Length: 25 pages
Date of creation: Aug 2005
Date of revision: Dec 2005
Handle: RePEc:hum:wpaper:sfb649dp2005-038

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Related research

Keywords: Markov; Markov chain; time dynamics; stochastic control problem;

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  1. Raouf Boucekkine & Omar Licandro & Luis A. Puch & Fernando del Rio, 2003. "Vintage capital and the dynamics of the AK model," Documentos de Trabajo del ICAE 0310, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
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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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