Continuous dependence estimates for viscosity solutions of integro-PDEs

  • Espen R. Jakobsena, Kenneth H. Karlsenb
  • Published 2005

Abstract

We present a general framework for deriving continuous dependence estimates for, possibly polynomially growing, viscosity solutions of fully nonlinear degenerate parabolic integro-PDEs. We use this framework to provide explicit estimates for the continuous dependence on the coefficients and the “Lévy measure” in the Bellman/Isaacs integro-PDEs arising in stochastic control/differential games. Moreover, these explicit estimates are used to prove regularity results and rates of convergence for some singular perturbation problems. Finally, we illustrate our results on some integro-PDEs arising when attempting to price European/American options in an incomplete stock market driven by a geometric Lévy process. Many of the results obtained herein are new even in the convex case where stochastic control theory provides an alternative to our pure PDE methods. © 2004 Elsevier Inc. All rights reserved.

Cite this paper

@inproceedings{Jakobsena2005ContinuousDE, title={Continuous dependence estimates for viscosity solutions of integro-PDEs}, author={Espen R. Jakobsena and Kenneth H. Karlsenb}, year={2005} }