Double Telegraph Processes and Complete Market Models

The traditional jump-telegraph processes are based on a Poisson process with alternating intensities. We develop a new model based on an alternating doubly stochastic Poisson process with random intensities of jumps. Moreover, in this model the jump-telegraph process performs additional jumps each t...

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Detalles Bibliográficos
Autor Principal: Ratanov, Nikita
Formato: Artículo (Article)
Lenguaje:Inglés (English)
Publicado: Taylor and Francis Inc. 2014
Materias:
Acceso en línea:https://repository.urosario.edu.co/handle/10336/23337
https://doi.org/10.1080/07362994.2014.899914
Descripción
Sumario:The traditional jump-telegraph processes are based on a Poisson process with alternating intensities. We develop a new model based on an alternating doubly stochastic Poisson process with random intensities of jumps. Moreover, in this model the jump-telegraph process performs additional jumps each time when the intensity changes at random. Martingale measures for this type of processes are described by using Girsanov's transformation. The market model based on the doubly stochastic jump-telegraph process is studied. A class of complete models is also considered. 2014 © Taylor and Francis Group, LLC.