A class of bivariate Erlang distributions and ruin probabilities in multivariate risk models
In this contribution, we introduce a new class of bivariate distributions of Marshall-Olkin type, called bivariate Erlang distributions. The Laplace transform, product moments and conditional densities are derived. Potential applications of bivariate Erlang distributions in life insurance and finance are considered. Further, our research project is devoted to the study of multivariate risk processes, which may be useful in analyzing ruin problems for insurance companies with a portfolio of dependent classes of business. We apply results from the theory of piecewise deterministic Markov processes in order to derive exponential martingales needed to establish computable upper bounds of the ruin probabilities, as their exact expressions are intractable.
Copules Erlang distribution Expectation-Maximization algorithm Piecewise deterministic Markov processes Multivariate risk model Ruin probability Poisson model with common shocks Renewal processes Copulas