A New Convergent Explicit Tree-Grid Method for HJB Equations in One Space Dimension

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

Keywords:   

Author Details

Matthias Ehrhardt

Michael Günther

Igor Kossaczký

Matthias Ehrhardt

Michael Günther

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