Analytic approach to solve a degenerate PDE for the Heston model.

We present an analytic approach to solve a degenerate parabolic problem associated with the Heston model, which is widely used in mathematical finance to derive the price of an European option on an risky asset with stochastic volatility. We give a variational formulation, involvingweighted Sobolev spaces, of the second-order degenerate elliptic operator of the parabolic PDE.We use this approach to prove, under appropriate assumptions on someinvolved unknownparameters, the existence and uniqueness of weak solutions to the parabolic problem on unbounded subdomains of the half-plane.