Spatial Approximation of Nondivergent Type Parabolic PDEs with Unbounded Coefficients Related to Finance

Abstract EN

We study the spatial discretisation of the Cauchy problem for a multidimensional linear parabolic PDE of second order, with nondivergent operator and unbounded time- and space-dependent coefficients.

The equation free term and the initial data are also allowed to grow.

Under a nondegeneracy assumption, we consider the PDE solvability in the framework of the variational approach and approximate in space the PDE problem's generalised solution, with the use of finite-difference methods.

The rate of convergence is estimated.