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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| 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 |
| 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. |
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