An Introduction to Finite Diffference Methods for PDEs in Finance
Book Chapter: Nizar Touzi, Optimal Stochastic Target problems, and Backward SDE, Fields Institute Monographs, 29, Springer, 2013, pp. 201-212.
18 Pages Posted: 16 Feb 2014 Last revised: 21 Feb 2014
Date Written: March 22, 2011
Abstract
I discuss in an elementary manner the practical aspects of designing monotone Finite Difference schemes for Hamilton-Jacobi-Bellman equations arising in Quantitative Finance. These are nonlinear equations for which classic Finite Difference methods may fail to converge to the correct solution. The approach based on the theory of viscosity solutions allows us to construct robust numerical approximations.
Keywords: Partial Differential Equations in Finance, Monotone Finite Difference methods, viscosity solutions
JEL Classification: C63, C61
Suggested Citation: Suggested Citation