Publicação
On the space discretization of PDES with unbounded coefficients arising in financial mathematics – the case of one spatial dimension
| Resumo: | 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. |
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| Autores principais: | Gonçalves, F. F. |
| Outros Autores: | Grossinho, Maria do Rosário; Morais, E. |
| Assunto: | Financial Mathematics Option Pricing Differential Equations Stochastic Methods Cauchy Problem |
| Ano: | 2010 |
| País: | Portugal |
| Tipo de documento: | preprint |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório da Universidade de Lisboa |
| Resumo: | 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. |
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