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

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 assumpti...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2014-01, Vol.2014 (2014), p.589-599-1359
Main Authors: Gonçalves, Fernando F., Grossinho, Maria Rosário
Format: Article
Language:English
Subjects:
Approximation
Cauchy problem
Convergence
Eulers equations
Finance
Finite difference method
Mathematical analysis
Operators
Partial differential equations
Stochastic models
Studies
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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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/801059