A Generalized Osgood Condition for Viscosity Solutions to Fully Nonlinear Parabolic Degenerate Equations

Abstract

Using a generalized assumption of Osgood type, we prove a comparison result between viscosity sub and supersolutions of fully nonlinear, possibly strongly degenerate, parabolic equations under rather generale assumtpions. The principle allows to consider dependence on the gradient witha quadratic growth and also on complex zeroth-order terms. The result it applies in particular to a differential model for pricing Mortgage-Backed Securities.