English

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