A Wiener-Hopf Monte Carlo Simulation Technique for Lévy Processes

W e develop a new method for simulating the joint law of the position and running maximum at a fixed time of a general L ́evy process with a view to application in insurance and financial mathematics. Although different, our method takes lessons from Carr’s so-called ‘Canadization’ technique as well...

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Detalles Bibliográficos
Autor: JUAN CARLOS PARDO MILLAN
Tipo de recurso: informe técnico
Estado:Versión publicada
Fecha de publicación:2010
País:México
Institución:Centro de Investigación en Matemáticas
Repositorio:Repositorio Institucional CIMAT
Idioma:inglés
OAI Identifier:oai:cimat.repositorioinstitucional.mx:1008/599
Acceso en línea:http://cimat.repositorioinstitucional.mx/jspui/handle/1008/599
Access Level:acceso abierto
Palabra clave:info:eu-repo/classification/MSC/Procesos de Levy
info:eu-repo/classification/cti/1
info:eu-repo/classification/cti/12
info:eu-repo/classification/cti/1208
info:eu-repo/classification/cti/120806
Descripción
Sumario:W e develop a new method for simulating the joint law of the position and running maximum at a fixed time of a general L ́evy process with a view to application in insurance and financial mathematics. Although different, our method takes lessons from Carr’s so-called ‘Canadization’ technique as well as Doney’s method of stochas- tic bounds for L ́evy processes; see Carr [6] and Doney [8]. We rely fundamentally on the Wiener-Hopf decomposition for L ́evy processes as well as taking advantage of recent developments in factorisation techniques of the latter theory due to Vigon [20] and Kuznetsov [11]. We illustrate our Wiener-Hopf Monte Carlo method on a number of different processes, including a new family of L ́evy processes called hypergeometric L ́evy processes.