Extrapolation discontinuous Galerkin method for ultraparabolic equations

Ultraparabolic equations arise from the characterization of the performance index of stochastic optimal control relative to Ultradiffusion processes; they evidence multiple temporal variables and may be regarded as parabolic along characteristic directions. We consider theoretical and approximation aspects of a temporally order and step size adaptive extrapolation discontinuous Galerkin method coupled with a spatial Lagrange second-order finite element approximation for a prototype ultraparabolic problem. As an application, we Value a so-called Asian option from mathematical finance. (c) 2008 Elsevier B.V. All rights reserved.