This article presents the Exponential-Generalized Inverse Gaussian regression model with varying dispersion and shape. The EGIG is a general distribution family which, under the adopted modelling framework, can provide the appropriate level of flexibility to fit moderate costs with high...

In insurance and related industries including healthcare, it is common to have several outcome measures that the analyst wishes to understand using explanatory variables. For example, in automobile insurance, an accident may result in payments for damage to one's own vehicle, damage to another...

We present some new evidence on the tail distribution of commercial property losses based on a recently constructed dataset on large commercial risks. The dataset is based on contributions from Lloyd’s of London syndicates, and provides information on over three thousand claims occurred during...

This article presents the Poisson-Inverse Gamma regression model with varying dispersion for approximating heavy-tailed and overdispersed claim counts. Our main contribution is that we develop an Expectation-Maximization (EM) type algorithm for maximum likelihood (ML) estimation of the...

Since its origins and numerous applications in material science, the Birnbaum–Saunders family of distributions has now found widespread uses in some areas of the applied sciences such as agriculture, environment and medicine, as well as in quality control, among others. It is able to model...

In a bonus-malus system in car insurance, the bonus class of a customer is updated from one year to the next as a function of the current class and the number of claims in the year (assumed Poisson). Thus the sequence of classes of a customer in consecutive years forms a Markov chain, and most...

Assume that claims in a portfolio of insurance contracts are described by independent and identically distributed random variables with regularly varying tails and occur according to a near mixed Poisson process. We provide a collection of results pertaining to the joint asymptotic Laplace...

With the record high leverage across all segments of the (global) economy, default prediction has never been more important. The excess cash illusion created in the context of COVID-19 may disappear just as quickly as the pandemic entered our world in 2020. In this paper, instead of using any...

In this paper, we discuss a generalization of the collective risk model and of Panjer's recursion. The model we consider consists of several business lines with dependent claim numbers. The distributions of the claim numbers are assumed to be Poisson mixture distributions. We let the claim...

For evaluating the probabilities of arbitrary random events with respect to a given multivariate probability distribution, specific techniques are of great interest. An important two-dimensional high risk limit law is the Gauss-exponential distribution whose probabilities can be dealt with based...