Work

On viscosity solutions of path dependent PDEs

Year: 2014

Type: article

Abstract: In this paper we propose a notion of viscosity solutions for path dependent semi-linear parabolic PDEs. This can also be viewed as viscosity solutions of non-Markovian backward SDEs, and thus extends the well-known nonlinear Feynman–Kac formula to non-Markovian case. We shall prove the existence, uniqueness, stability and comparison principle for the viscosity solutions. The key ingredient of our approach is a functional Itô calculus recently introduced by Dupire [Functional Itô calculus (2009) Preprint].

Source: The Annals of Probability

DOI: 10.1214/12-aop788

Authors: Ibrahim Ekren, Christian Keller, Nizar Touzi, Jianfeng Zhang

Institutions: University of Southern California, École Polytechnique, Centre de Mathématiques Appliquées de l'École polytechnique

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: bronze

Funders: National Science Foundation, Fondation du Risque

Award: Collaborative Research: Applications of Stochastic Analysis to Models of Multi-Agent Interactions