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 - <p style="text-align: justify;">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.&nbsp;</p>