Preprint 2004-036

Continuous Dependence Estimates for Viscosity Solutions of Integro-PDEs

Espen R. Jakobsen and Kenneth H. Karlsen

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 ``L\'evy 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 L\'evy process. Many of the results obtained herein are new even in the convex case where stochastic control

Available as PDF (336 Kbytes).
Espen R. Jakobsen, <>
Kenneth H. Karlsen, <>
Publishing information:
To appear in J. of Differential Equations
Submitted by:
<> July 7 2004.

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