PDE Solutions of Stochastic Differential Utility

This paper presents conditions for the existence and properties of stochastic differential utility as a solution of a partial differential equation. Stochastic differential utility is an extension of the classical additively-separable utility model that is designed as a platform for new financial asset pricing results. The extension is important, for example, when investors display preference for early or late resolution of uncertainty. The existence conditions admit Kreps-Porteus stochastic differential utility.