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Title:Regression methods for stochastic control problems and their convergence analysis PDF Logo
Authors:Belomestny, Denis
Kolodko, Anastasia
Schoenmakers, John G. M.
Issue Date:2009
Series/Report no.:SFB 649 discussion paper 2009,026
Abstract:In this paper we develop several regression algorithms for solving general stochastic optimal control problems via Monte Carlo. This type of algorithms is particularly useful for problems with a highdimensional 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 some assumptions. Finally, the presented methods are applied in a numerical example of a high-dimensional controlled Bermudan basket option in a financial market with a large investor.
Subjects:Optimal stochastic control
Regression methods
Convergence analysis.
JEL:R12
Document Type:Working Paper
Appears in Collections:SFB 649 Discussion Papers, HU Berlin

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