Semi-Lagrangian schemes for linear and fully non-linear Hamilton-Jacobi-Bellman equations
Numerical Analysis
2014-05-26 v1
Abstract
We consider the numerical solution of Hamilton-Jacobi-Bellman equations arising in stochastic control theory. We introduce a class of monotone approximation schemes relying on monotone interpolation. These schemes converge under very weak assumptions, including the case of arbitrary degenerate diffusions. Besides providing a unifying framework that includes several known first order accurate schemes, stability and convergence results are given, along with two different robust error estimates. Finally, the method is applied to a super-replication problem from finance.
Keywords
Cite
@article{arxiv.1403.1217,
title = {Semi-Lagrangian schemes for linear and fully non-linear Hamilton-Jacobi-Bellman equations},
author = {Kristian Debrabant and Espen R. Jakobsen},
journal= {arXiv preprint arXiv:1403.1217},
year = {2014}
}
Comments
to appear in the proceedings of HYP2012