# Duality in ruin problems for ordered risk models

*Pierre-Olivier Goffard* and
*Claude Lefèvre*

*Insurance: Mathematics and Economics*, 2018, vol. 78, issue C, 44-52

**Abstract:**
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. Lefèvre and Picard (2011) 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.

**Keywords:** Primal and dual risk models; Order statistic property; Ruin problems; Appell and Abel-Gontcharov polynomials; Level spacings (search for similar items in EconPapers)

**Date:** 2018

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:insuma:v:78:y:2018:i:c:p:44-52

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