Applications of Erlang Mixtures in Actuarial Science

Dr. X. Sheldon Lin, Department of Statistics University of Toronto, April 8, 2011

In this talk I will discuss analytical and computational properties of univariate and multivariate Erlang mixtures and the applications of these mixtures in actuarial science. The first half of the talk will focus on the class of univariate Erlang mixtures. I will show that the class is larger that it appears. I will next propose an EM algorithm for estimation of finite Erlang mixtures. Performance of the algorithm is tested using simulated and real insurance data. Distributional and moment properties are then discussed in the context of insurance risk analysis.

In the second half of the talk I will introduce a class of multivariate Erlang mixtures each of which is conditionally independent. I would argue that such a multivariate Erlang mixture could be an ideal parametric model for modeling multivariate risks in insurance, especially when modelling dependence is a concern, as the class is dense in the space of positive continuous multivariate distributions and an EM algorithm, similar to the univariate case, for estimation is available. I will also show that the class has many desirable properties. Finally I will introduce a new notion called quasi-comonotonicity that can be useful to identify upper and lower bounds in a multivariate stochastic order and to construct a multivariate dependence model.

This talk is based on some recent papers with my collaborators Gordon Willmot and Simon Lee.