NDLI: Regression Methods for Stochastic Control Problems and Their Convergence Analysis

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Schoenmakers, John Kolodko, Anastasia Belomestny, Denis
Copyright Year	2010
Abstract	In this paper we develop several regression algorithms for solving general stochastic optimal control problems via Monte Carlo. This type of algorithm is particularly 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 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.
Starting Page	3562
Ending Page	3588
Page Count	27
File Format	PDF
ISSN	03630129
DOI	10.1137/090752651
e-ISSN	10957138
Issue Number	5
Volume Number	48
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2010-03-03
Access Restriction	Subscribed
Subject Keyword	regression methods Monte Carlo methods convergence analysis optimal stochastic control Stopping times; optimal stopping problems; gambling theory
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Applied Mathematics

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