The focus of this book is on the two major areas of risk theory: aggregate claims distributions
and ruin theory. For aggregate claims distributions, detailed descriptions are given of …

In this paper we suggest the use of mixtures of Erlang distributions with common scale
parameter to model insurance losses. A modified expectation-maximization (EM) algorithm …

A wide variety of distributions are shown to be of mixed-Erlang type. Useful computational
formulas result for many quantities of interest in a risk-theoretic context when the claim size …

A review of analytical and computational properties of the mixed Erlang distribution is given
in the context of risk analysis. Basic distributional properties are discussed, and examples of …

In this paper, we extend the concept of ruin in risk theory to the Parisian type of ruin. For this
to occur, the surplus process must fall below zero and stay negative for a continuous time …

In this paper we consider an extension of the two-dimensional risk model introduced in
Avram, Palmowski and Pistorius (2008a). To this end, we assume that there are two …

This monograph is a summary of our view of the current state of the art with respect to the
analysis of surplus and ruin-theoretic analysis for the class of Sparre Andersen (renewal) …

In this paper we study the finite-time expected discounted penalty function (EDPF) and its
decomposition in the classical risk model perturbed by diffusion. We first give the solution to …

In this paper, we revisit the finite-time ruin probability in the classical compound Poisson risk
model. Traditional general solutions to finite-time ruin problems are usually expressed in …

This paper studies a numerical method based on Legendre polynomials and extreme
learning machine algorithm to solve the ruin probabilities in the classical risk model and the …