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Duality in ruin problems for ordered risk models

Author

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  • Pierre-Olivier Goffard

    (UCSB - UCSB - UC Santa Barbara - University of California [Santa Barbara] - UC - University of California)

  • Claude Lefèvre

    (ULB - Département de Mathématique [Bruxelles] - ULB - Faculté des Sciences [Bruxelles] - ULB - Université libre de Bruxelles)

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. 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.

Suggested Citation

  • Pierre-Olivier Goffard & Claude Lefèvre, 2018. "Duality in ruin problems for ordered risk models," Post-Print hal-01398910, HAL.
    • Handle: RePEc:hal:journl:hal-01398910
    DOI: 10.1016/j.insmatheco.2017.11.005
    Note: View the original document on HAL open archive server: https://hal.science/hal-01398910v2
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    References listed on IDEAS

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