Parameter estimation of a bivariate compound Poisson process |
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Authors: | Habib Esmaeili,Claudia Klü ppelberg |
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Affiliation: | a Center for Mathematical Sciences, Technische Universität München, D-85748 Garching, Germany b Institute for Advanced Study, Technische Universität München, D-85748 Garching, Germany |
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Abstract: | In this article, we review the concept of a Lévy copula to describe the dependence structure of a bivariate compound Poisson process. In this first statistical approach we consider a parametric model for the Lévy copula and estimate the parameters of the full dependent model based on a maximum likelihood approach. This approach ensures that the estimated model remains in the class of multivariate compound Poisson processes. A simulation study investigates the small sample behaviour of the MLEs, where we also suggest a new simulation algorithm. Finally, we apply our method to Danish fire insurance data. |
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Keywords: | primary, 62M05, 62P05 secondary, 60G51 |
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