An Exact Connection between two Solvable SDEs and a Nonlinear Utility Stochastic PDE

Nicole El Karoui, Mohamed Mrad

Motivated by the work of Musiela and Zariphopoulou \cite{zar-03}, we study the Itô random fields which are utility functions $U(t,x)$ for any $(\omega ,t)$. The main tool is the marginal…