We prove existence, uniqueness and gradient estimates of stochastic differential utility as a solution of the Cauchy problem for degenerate nonlinear partial differential equation. We also characterize the solution in the vanishing viscosity sense.

We examine a recent model, proposed by Hobson and Rogers, which generalizes the classical one by Black and Scholes for pricing derivative securities such as options and futures. We treat the numerical solution of some degenerate partial differential equations governing this financial problem and...

The path-dependent volatility model by Hobson and Rogers is considered. It is known that this model can potentially reproduce the observed smile and skew patterns of different directions, while preserving the completeness of the market. In order to quantitatively investigate the pricing...