Publicação
Numerical approximation of multidimensional parabolic partial differential equations arising in financial mathematics
| Resumo: | In many cases, financial option pricing models give rise to PDEs which turn out to be very difficult to solve by classical analytic tools. In this article, we study the numerical approximation in space of the solution of the Cauchy problem for a multidimensional linear parabolic PDE of second order, with time and space-dependent coefficients. Making use of the L 2 theory of solvability in Sobolev spaces, the solution of the PDE problem is approximated in space, with finite-difference methods. The rate of convergence is estimated. |
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| Autores principais: | Gonçalves, Fernando F. |
| Outros Autores: | Grossinho, Maria do Rosário |
| Assunto: | Financial Option Pricing Finite-difference Methods Cauchy Problem Parabolic Partial Differential Equations Multi-dimensional Equations |
| Ano: | 2009 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório da Universidade de Lisboa |
| Resumo: | In many cases, financial option pricing models give rise to PDEs which turn out to be very difficult to solve by classical analytic tools. In this article, we study the numerical approximation in space of the solution of the Cauchy problem for a multidimensional linear parabolic PDE of second order, with time and space-dependent coefficients. Making use of the L 2 theory of solvability in Sobolev spaces, the solution of the PDE problem is approximated in space, with finite-difference methods. The rate of convergence is estimated. |
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