Optimal prevention of large risks with two types of claims

Romain Gauchon (1) , Stéphane Loisel (1) , Jean-Louis Rullière (1) , Julien Trufin (2)

1 SAF - Laboratoire de Sciences Actuarielle et Financière
2 Département de mathématiques Université Libre de Bruxelles

In this paper, we propose and study a risk model with two types of claims in which the insurer may invest into a prevention plan which decreases the intensity of large claims without impacting the small claims. We identify a necessary and sufficient condition for insurers to use prevention if there is no surplus. If, in addition, the severity of large claims dominates that of small claims by the harmonic mean residual life (HMRL) order, insurers invest more in prevention in the presence of a surplus. Finally, we characterize the asymptotic optimal prevention strategy when the initial surplus tends to infinity in the two main cases where both claim types are light-tailed and where one of them is light-tailed and the other one is heavy-tailed.

Mots clés: Ruin theory; Prevention; Optimal prevention strategy; Insurance

Domaines: Gestion des risques [q-fin.RM]; Probabilités [math.PR]; Optimisation et contrôle [math.OC]

Romain Gauchon, Stéphane Loisel, Jean-Louis Rullière, Julien Trufin. Optimal prevention of large risks with two types of claims. Scandinavian Actuarial Journal, In press. ⟨hal-02314914v2⟩