Spatial approximation of nondivergent type parabolic PDEs with unbounded coefficients related to finance. (English) Zbl 1474.65274

Summary: 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.


65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
35A35 Theoretical approximation in context of PDEs
91G60 Numerical methods (including Monte Carlo methods)
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