Continuous dependence estimates for viscosity solutions of integro-PDEs

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:212

Article

Jakobsen, ER ; Karlsen, KH

关键词: nonlinear degenerate parabolic integro-partial differential equation;    Bellman equation;    Isaacs equation;    viscosity solution;    continuous dependence estimate;    regularity;    vanishing viscosity method;    convergence rate;   

DOI  :  10.1016/j.jde.2004.06.021

来源: Elsevier

【 摘 要 】

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 Levy 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 Levy 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. (c) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free