On a Bivariate Poisson Negative Binomial Risk Process
DOI:
https://doi.org/10.11145/103Abstract
In this paper we define a bivariate counting process as a compound Poisson process with bivariate negative binomial compounding distribution. We investigate some of its basic properties, recursion formulas and probability mass function. Then we consider a risk model in which the claim counting process is the defined bivariate Poisson negative binomial process. For the defined risk model we derive the joint distribution of the time to ruin and the deficit at ruin as well as the ruin probability. We discuss in detail the particular case of exponentially distributed claims.
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Acknowledgements: This work was supported by the European So-cial Fund through the Human Resource Development Operational Pro-gramme under contract BG051PO001-3.3.06-0052 (2012/2014).
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