A generalized Osgood condition for viscosity solutions to fully nonlinear parabolic degenerate equations

Abstract

Using a generalized assumption of Osgood type, we prove a new comparison result for viscosity sub and supersolutions of fully nonlinear, possibly degenerate, parabolic equations. Our result allows to deal with hamiltonian functions with a quadratic growth in the spatial gradient, under special compatibility conditions with the diffusive terms. It applies in particular to a financial differential model for pricing Mortgage-Backed Securities.