Representation Formula for Viscosity Solutions to a class of Nonlinear Parabolic PDEs

2021/06/22 by Marco Pozza, Pozza, Marco
Economics, Econometrics and Finance · Mathematics · Engineering · #Stochastic processes and financial applications #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2106.11671

Abstract

We provide a representation formula for viscosity solutions to a class of nonlinear second order parabolic PDEs given as a sup--envelope function. This is done through a dynamic programming principle derived from Denis, Hu, Peng (2010). The formula can be seen as a nonlinear extension of the Feynman--Kac formula and is based on the backward stochastic differential equations theory.

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