Finite-Time Ruin Probabilities for Discrete, Possibly Dependent, Claim Severities

Stéphane Loisel (1) , Claude Lefèvre (2)

1 SAF - Laboratoire de Sciences Actuarielle et Financière
2 ULB - Département de Mathématique [Bruxelles]

This paper is concerned with the compound Poisson risk model and two generalized models with still Poisson claim arrivals. One extension incorporates inhomogeneity in the premium input and in the claim arrival process, while the other takes into account possible dependence between the successive claim amounts. The problem under study for these risk models is the evaluation of the probabilities of (non-)ruin over any horizon of finite length. The main recent methods, exact or approximate, used to compute the ruin probabilities are reviewed and discussed in a unified way. Special attention is then paid to an analysis of the qualitative impact of dependence between claim amounts.

Mots clés: non-stationary claim arrivals; interdependent claim amounts; impact of dependence; comonotonic risks; heavy-tailed distributions; compound Poisson model; ruin probability; finite-time horizon; recursive methods; (generalized) Appell polynomials; non-constant premium

Domaines: Economies et finances; Probabilités [math.PR]

Stéphane Loisel, Claude Lefèvre. Finite-Time Ruin Probabilities for Discrete, Possibly Dependent, Claim Severities. Methodology and Computing in Applied Probability, 2009, 11 (3), pp.425-441. ⟨10.1007/s11009-009-9123-9⟩. ⟨hal-00201377⟩