In this paper, a study of a stochastic volatility model for asset pricing is described. Originally presented by J. Da Fonseca, M. Grasselli and C. Tebaldi, the Wishart volatility model identifies the volatility of the asset as the trace of a Wishart process. Contrary to a classic multifactor...

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 utility $U_x(t,x)$ and its inverse expressed as the opposite of the derivative of the Fenchel conjuguate...