Dependent binomial distribution and its application in reinsurance and credits

The paper is devoted to the dependent binomial distribution. The assumption of independence of the random variables in the classical binomial distribution is omitted, so we obtain a more realistic situation. The definition and basic properties of such distribution are presented. The dependent structure of the random variables is characterized by the copula. The cases, which are dependent on the different copulas: exchangeable, independent, comonotonicity, the mixture of such copulas, and Archimedean, are studied. The two extensions of our model, i.e., the values of process and the random number of variables, are investigated, too. The applications of the dependent binomial distribution to the excess-of-loss reinsurance and the credit risk management are presented.