Volume 11, Issue 1
A New Convergent Explicit Tree-Grid Method for HJB Equations in One Space Dimension

Igor Kossaczký, Matthias Ehrhardt & Michael Günther

Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 1-29.

Published online: 2018-11

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  • 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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@Article{NMTMA-11-1, author = {Kossaczký , Igor and Ehrhardt , Matthias and Günther , Michael}, title = {A New Convergent Explicit Tree-Grid Method for HJB Equations in One Space Dimension }, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {11}, number = {1}, pages = {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. 

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0066}, url = {http://global-sci.org/intro/article_detail/nmtma/10641.html} }
TY - JOUR T1 - A New Convergent Explicit Tree-Grid Method for HJB Equations in One Space Dimension AU - Kossaczký , Igor AU - Ehrhardt , Matthias AU - Günther , Michael JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 1 EP - 29 PY - 2018 DA - 2018/11 SN - 11 DO - http://doi.org/10.4208/nmtma.OA-2017-0066 UR - https://global-sci.org/intro/article_detail/nmtma/10641.html KW - AB -

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. 

Igor Kossaczký, Matthias Ehrhardt & Michael Günther. (2020). A New Convergent Explicit Tree-Grid Method for HJB Equations in One Space Dimension . Numerical Mathematics: Theory, Methods and Applications. 11 (1). 1-29. doi:10.4208/nmtma.OA-2017-0066
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