In this paper, based on the additive measure integral representation of a non-additive measure integral, it is shown that any comonotonically additive premium principle can be represented as an integral of the distorted decumulative distribution function of the insurance risk. Furthermore, a sufficient and necessary condition that a premium principle is a distortion premium principle is given.

The probability density function of the time of ruin in the classical model with exponential claim sizes is obtained directly by inversion of the associated Laplace transform. This result is then used to obtain explicit closed-form expressions for the moments. The form of the density is examined for various parameter choices.

In nonlife insurance, actuaries usually resort to random effects to take unexplained heterogeneity into account (in the spirit of the Bühlmann-Straub model). This paper aims to study the kind of dependence induced by the introduction of correlated latent variables in the annual numbers of claims reported by policyholders. The effect of reporting claims on the a posteriori distribution of the random effects will be made precise. This will be done by establishing some stochastic monotonicity property of the a posteriori distribution with respect to the claims history.

A three parameter Gaussian exponential approximation to some compound Poisson distributions is considered. It is constructed by specifying the reciprocal of the mean excess function as a linear affine function below some threshold and a positive constant above this threshold. As an analytical approximation to compound Poisson distributions, it is only feasible either for a limited range of the Poisson parameter or for higher coefficients of variation. A semiparametric determination of the unknown threshold parameter is proposed. The analysis of a real-life example from pension fund mathematics displays an improved quality of fit of the new model when compared with other simple good alternative approximations based on the zero gamma, translated gamma and zero translated gamma.

In this paper we revisit an economic model of Buhlmann (ASTIN Bulletin, 1980) and derive equilibrium pricing transforms. We obtain the Esscher Transform and the Wang Transform under different sets of assumptions on the aggregate economic environment. We show that the Esscher Transform and the Wang Transform exhibit very different behaviors when used in pricing insurance risks.

We estimate Value-at-Risk for sums of dependent random variables. We model multivariate dependent random variables using archimedean copulas. This structure allows one to calculate the asymptotic behaviour of extremal events. An important application of such results are Value-at-Risk estimates for sums of dependent random variables.

In this paper non-normal distributions via scale mixtures are introduced into insurance applications. The symmetric distributions of interest are the Student-t and exponential power (EP) distributions. A Bayesian approach is adopted with the aid of simulation to obtain posterior summaries. We shall show that the computational burden for the Bayesian calculations is alleviated via the scale mixtures representations. Illustrative examples are given.