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Type: Report × Subject: regression methods ×

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    Regression methods for stochastic control problems and their convergence analysis
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Belomestny, Denis; Kolodko, Anastasia; Schoenmakers, John G.M.
    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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    Regression methods in pricing American and Bermudan options using consumption processes
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Belomestny, Denis; Milstein, Grigor N.; Spokoiny, Vladimir
    Here we develop methods for efficient pricing multidimensional discrete-time American and Bermudan options by using regression based algorithms together with a new approach towards constructing upper bounds for the price of the option. Applying sample space with payoffs at the optimal stopping times, we propose sequential estimates for continuation values, values of the consumption process, and stopping times on the sample paths. The approach admits constructing both low and upper bounds for the price by Monte Carlo simulations. The methods are illustrated by pricing Bermudan swaptions and snowballs in the Libor market model.