{"id":74962,"date":"2018-03-09T23:20:04","date_gmt":"2018-03-09T23:20:04","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/numerical-analysis-of-second-order-lagrange-galerkin-schemes-application-to-option-pricing-problems\/"},"modified":"2018-03-09T23:20:04","modified_gmt":"2018-03-09T23:20:04","slug":"numerical-analysis-of-second-order-lagrange-galerkin-schemes-application-to-option-pricing-problems","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/numerical-analysis-of-second-order-lagrange-galerkin-schemes-application-to-option-pricing-problems\/","title":{"rendered":"Numerical analysis of second order lagrange-galerkin schemes. application to option pricing problems."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Mar\u00eda Rodr\u00edguez Nogueiras <\/strong><\/h2>\n<p>En esta tesis se estudia la resoluci\u00f3n num\u00e9rica de ecuaciones lineales, y no lineales, de tipo convecci\u00f3n-difusi\u00f3n-reacci\u00f3n mediante un m\u00e9todo de lagrange-galerkin de orden dos. El estudio ha sido motivado por una aplicaci\u00f3n en finanzas: la valoraci\u00f3n de productos financieros de tipo derivado usando ecuaciones en derivadas parciales.  m\u00e1s detalladamente, el m\u00e9todo de lagrange-galerkin se introduce usando el formalismo de la mec\u00e1nica de los medios continuos y formulaciones d\u00e9biles. despu\u00e9s, se establecen rigurosamente las propiedades de estabilidad y consistencia (orden dos) del algoritmo. Adem\u00e1s, se aborda el problema de la cuadratura num\u00e9rica, proponiendo f\u00f3rmulas de cuadratura para elementos finitos de lagrange, lineales y cuadr\u00e1ticos, que preservan la estabilidad del m\u00e9todo (como se comprueba mediante un an\u00e1lisis de fourier). Finalmente, se muestran algunos ejemplos num\u00e9ricos obtenidos mediante un c\u00f3digo implementado en fortran, que ilustran y completan nuestro an\u00e1lisis.  con respecto a la aplicaci\u00f3n en finanzas, se realiza una introducci\u00f3n a la modelizaci\u00f3n en finanzas en el marco de black-scholes, centr\u00e1ndonos en un tipo particular de opciones financieras: las opciones asi\u00e1ticas, para las que se deducen algunas propiedades originales y se formula el problema matem\u00e1tico de valoraci\u00f3n de las mismas.  en el caso de las opciones asi\u00e1ticas de tipo europeo, se realiza la resoluci\u00f3n num\u00e9rica del problema de valoraci\u00f3n empleando los m\u00e9todos de lagrange-galerkin analizados, atendiendo a las particularidades del problema concreto (por ejemplo, se optimiza la estructura algebraica del algoritmo).  en el caso de las opciones asi\u00e1ticas de tipo americano, su resoluci\u00f3n num\u00e9rica combina un algoritmo iterativo con los m\u00e9todos de lagrange-galerkin. M\u00e1s precisamente, se han comparado dos algoritmos basados en la formulaci\u00f3n mixta del problema: el algoritmo de berm\u00fadez-moreno y un algoritmo de conjunto activ<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Numerical analysis of second order lagrange-galerkin schemes. application to option pricing problems.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Numerical analysis of second order lagrange-galerkin schemes. application to option pricing problems. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Mar\u00eda Rodr\u00edguez Nogueiras <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Santiago de compostela<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 24\/06\/2005<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>varela Berm\u00fadez De Castro L\u00f3pez<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: ildefonso D\u00edaz <\/li>\n<li>fausto Saleri (vocal)<\/li>\n<li>peregrina Quintela (vocal)<\/li>\n<li>Luis Fern\u00e1ndez jos\u00e9 (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Mar\u00eda Rodr\u00edguez Nogueiras En esta tesis se estudia la resoluci\u00f3n num\u00e9rica de ecuaciones lineales, y no lineales, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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