Impact of correlation crises in risk theory

Romain Biard (1) , Claude Lefèvre (2) , Stéphane Loisel (1)

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

In the renewal risk model, several strong hypotheses may be found too restrictive to model accurately the complex evolution of the reserves of an insurance company. In the case where claim sizes are heavy-tailed, we relax independence and stationarity assumptions and extend some asymptotic results on finite-time ruin probabilities, to take into account possible correlation crises like the one recently bred by the sub-prime crisis: claim amounts, in general assumed to be independent, may suddenly become strongly positively dependent. The impact of dependence and non-stationarity is analyzed and several concrete examples are given.

Mots clés: Finite-time ruin probabilities; ruin theory; correlation crisis; Sub-prime effect; processes with dependent increments; asymptotic behavior; non-stationarity; heavy-tailed claim size distribution

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

Romain Biard, Claude Lefèvre, Stéphane Loisel. Impact of correlation crises in risk theory: Asymptotics of finite-time ruin probabilities for heavy-tailed claim amounts when some independence and stationarity assumptions are relaxed. Insurance: Mathematics and Economics, 2008, 43 (3), pp.412-421. ⟨hal-00308782⟩