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A Picard-type Iteration for Backward Stochastic Differential Equations : Convergence and Importance Sampling

A Picard-type Iteration for Backward Stochastic Differential Equations : Convergence and Importance Sampling

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MOSELER, Thilo, 2010. A Picard-type Iteration for Backward Stochastic Differential Equations : Convergence and Importance Sampling

@phdthesis{Moseler2010Picar-644, title={A Picard-type Iteration for Backward Stochastic Differential Equations : Convergence and Importance Sampling}, year={2010}, author={Moseler, Thilo}, address={Konstanz}, school={Universität Konstanz} }

2011-03-22T17:45:20Z We consider a numerical scheme for backward stochastic differential equations which avoids nested conditional expectations backward in time.<br />In the first part we develop a variance reduced variant of the Picard-type scheme of C. Bender and R. Denk. This is in particular useful to compute more stable estimators for initial prices of option with nonstandard exercise features. We derive a directly implementable algorithm using importance sampling and prove convergence.<br />The second part of the thesis is devoted to a modification of the scheme C. Bender and R. Denk. We assume to have a bounded driver and a bounded terminal condition and prove an L²-error bound depending on the parameters which can be chosen by a user. These are in detail the number of Monte Carlo simulations, the time step size and the number of basis function used for projections.<br />Finally, we present in the third part numerical examples illustrating the effects of the importance sampling method and also test the application of nonparametric regression for the approximation of backward stochastic differential equations. 2011-03-22T17:45:20Z Moseler, Thilo A Picard-type Iteration for Backward Stochastic Differential Equations : Convergence and Importance Sampling Moseler, Thilo eng application/pdf Eine Iteration vom Picard-Typ für stochastische Rückwärts-Differentialgleichungen 2010 deposit-license

Dateiabrufe seit 01.10.2014 (Informationen über die Zugriffsstatistik)

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