Duality in ruin problems for ordered risk models

Pierre-Olivier Goffard (1) , Claude Lefèvre (2)

1 UCSB - UCSB
2 ULB - Département de Mathématique [Bruxelles]

The dual risk model is considered when the gain arrivals are governed by an order statistic point process (OSPP). The p.d.f. of the ruin time is obtained in terms of a remarkable family of polynomials. By duality, the p.d.f. of the ruin time is deduced for a Sparre-Andersen insurance risk model where the claim sizes are distributed as the inter-arrival times in an OSPP. On the other hand, duality is used again to derive the finite-time ruin probability in a dual model where the gains correspond to the inter-arrival times of an OSPP. MSC 2010: 60G55, 60G40, 12E10.

Mots clés: Order statistic property; Appell and Abel-Gontcharoff polynomials; Dual risk model; Time to ruin; Risk theory

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

Pierre-Olivier Goffard, Claude Lefèvre. Duality in ruin problems for ordered risk models. 2016. ⟨hal-01398910v1⟩