Duality in ruin problems for ordered risk models

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

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

On one hand, an ordered dual risk model is considered where the profit arrivals are governed by an order statistic point process (OSPP). First, the ruin time distribution is obtained in terms of Abel-Gontcharov polynomials. Then, by duality, the ruin time distribution is deduced for an insurance model where the claim amounts correspond to the inter-arrival times in an OSPP. On the other hand, an ordered insurance model is considered with an OSPP as claim arrival process. Lef\`evre and Picard \cite{LePi11} determined the finite-time ruin probability in terms of Appell polynomials. Duality is used to derive the ruin probability in a dual model where the profit sizes correspond to the inter-arrival times of an OSPP.

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. Insurance: Mathematics and Economics, 2018, 78, pp.44-52. ⟨10.1016/j.insmatheco.2017.11.005⟩. ⟨hal-01398910v2⟩