On the Space Discretization of Pdes with Unbounded Coefficients Arising in Financial Mathematics – the Case of One Spatial Dimension
نویسندگان
چکیده
We study the space discretization of the Cauchy problem for a second order linear parabolic PDE, with one spatial dimension and unbounded time and space-dependent coefficients. The PDE free term and the initial data are also allowed to grow. Under the assumption that the PDE does not degenerate, the problem’s weak solution is approximated in space, with finite-difference methods. The rate of convergence is estimated. A numerical example is given in order to illustrate the theoretical results.
منابع مشابه
Space Discretization of Pdes with Unbounded Coefficients Connected to Option Pricing – the Case of One Spatial Dimension
We study the space discretization of the Cauchy problem for a second order linear parabolic PDE, with one spatial dimension 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 probl...
متن کاملSpace Discretization of Pdes with Unbounded Coefficients Connected to Option Pricing – the Case of One Spacial Dimension
We study the space discretization of the Cauchy problem for a second order linear parabolic PDE, with one spacial dimension 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 probl...
متن کاملSolving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation
In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...
متن کاملSolution to time fractional generalized KdV of order 2q+1 and system of space fractional PDEs
Abstract. In this work, it has been shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve time fractional generalized KdV of order 2q+1 and certain fractional PDEs. It is shown that exponential operators are an effective method for solving certain fractional linear equations with non-constant coefficients. It may be concluded that the com...
متن کاملComponents Affecting the Resilience of Historical Bazaars Space with Emphasis on Capabilities of the Physical-Functional Dimension of Space Case Study: Amir Complex at Tabriz Historical Bazaar
Problem statement: The concept of resilience has long been published to explain how different types of systems respond to unexpected shocks, and research on resilience of environments to abnormal hazards has just begun, requiring extensive reflection and consideration. Spatial resilience thinking is as one of the new dimensions in the field of resilience and architecture. This dimension seeks t...
متن کامل