Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9501589 | Journal of Differential Equations | 2005 | 41 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Espen R. Jakobsen, Kenneth H. Karlsen,