This article considers goodness-of-fit tests for bivariate INAR and bivariate Poisson autoregression models. The test statistics are based on an L2-type distance between two estimators of the probability generating function of the observations: one being entirely nonparametric and the second one...

The distribution-free chain ladder reserving method belongs to the most frequently used approaches in general insurance. It is well known, see Mack (1993), that the estimators f̂j of the development factors are unbiased and mutually uncorrelated under some mild conditions on the mean structure...

A common approach to the claims reserving problem is based on generalized linear models (GLM), where the claims in different origin and development years are assumed to be independent variables. If this is violated, the classical techniques may provide incorrect predictions of the claims...

We derive the variance of the duration of play in the classical gambler’s ruin problem of two players with ties allowed. The variance of the game duration for the three-tower problem, one of the possible extensions of the game for the case of three players, is presented as well.