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Regression methods for stochastic control problems and their convergence analysis

Please always quote using this URN:urn:nbn:de:0296-matheon-5420
  • In this paper we develop several regression algorithms for solving general stochastic optimal control problems via Monte Carlo. This type of algorithms is particulary useful for problems with a high-dimensional state space and complex dependence structure of the underlying Markov process with respect to some control. The main idea behind the algorithms is to simulate a set of trajectories under some reference measure and to use the Bellman principle combined with fast methods for approximating conditional expectations and functional optimization. Theoretical properties of the presented algorithms are investigated and the convergence to the optimal solution is proved under mild assumptions. Finally, we present numerical results for the problem of pricing a high-dimensional Bermudan basket option under transaction costs in a financial market with a large investor.

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Metadaten
Author:Denis Belomestny, Anastasia Kolodko, John Schoenmakers
URN:urn:nbn:de:0296-matheon-5420
Referee:Peter Imkeller
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2009/01/20
Release Date:2009/01/19
Preprint Number:538
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