A New Convergent Explicit Tree-Grid Method for HJB Equations in One Space Dimension
Year: 2018
Author: Matthias Ehrhardt, Michael Günther, Igor Kossaczký, Matthias Ehrhardt, Michael Günther
Numerical Mathematics: Theory, Methods and Applications, Vol. 11 (2018), Iss. 1 : pp. 1–29
Abstract
In this work we introduce a new unconditionally convergent explicit Tree-Grid Method for solving stochastic control problems with one space and one time dimension or equivalently, the corresponding Hamilton-Jacobi-Bellman equation. We prove the convergence of the method and outline the relationships to other numerical methods. The case of vanishing diffusion is treated by introducing an artificial diffusion term. We illustrate the superiority of our method to the standardly used implicit finite difference method on two numerical examples from finance.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2017-0066
Numerical Mathematics: Theory, Methods and Applications, Vol. 11 (2018), Iss. 1 : pp. 1–29
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Author Details
Matthias Ehrhardt Email
Michael Günther Email
Igor Kossaczký Email
Matthias Ehrhardt Email
Michael Günther Email
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