Preprint 2004-036

Continuous Dependence Estimates for Viscosity Solutions of Integro-PDEs

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

Paper:

Available as PDF (336 Kbytes).

Author(s):

Espen R. Jakobsen, <erj@math.uio.no>

Kenneth H. Karlsen, <kennethk@math.uio.no>

Publishing information:

To appear in J. of Differential Equations

Comments:

Submitted by:

<kennethk@math.uio.no> July 7 2004.