M. Mercè Claramunt

Ruin problems for a discrete time risk model with non-homogeneous conditions

This paper is concerned with a non-homogeneous discrete time risk model where premiums are fixed but non-uniform, and claim amounts are independent but non-stationary. It allows one to account for the influence of inflation and interest and the effect of variability in the claims. Our main purpose is to develop an algorithm for calculating the finite time ruin probabilities and the associated ruin severity distributions. The ruin probabilities are shown to rely on an underlying algebraic structure of Appell type. That property makes the computational method proposed quite simple and efficient. Its application is illustrated through some numerical examples of ruin problems. The well known Lundberg bound for ultimate ruin probabilities is also reexamined within such a non-homogeneous framework.

Allocation of solvency cost in group annuities: Actuarial principles and cooperative game theory

Abstract This article will compare two methods of allocating solvency cost: the first based on actuarial principles; the second based on Cooperative Game theory. The consistency of the actuarial principles will be analysed by looking at the rationality of the allocation. Two numeric applications will also be made.

Equilibrium distributions and discrete Schur-constant models

This paper introduces Schur-constant equilibrium distribution models of dimension n for arithmetic non-negative random variables. Such a model is defined through the (several orders) equilibrium distributions of a univariate survival function. First, the bivariate case is considered and analyzed in depth, stressing the main characteristics of the Poisson case. The analysis is then extended to the multivariate case. Several properties are derived, including the implicit correlation and the distribution of the sum.