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Ruin problems under IBNR dynamics

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  • Julien Trufin
  • Hansjörg Albrecher
  • Michel Denuit

Abstract

In this paper, we consider a discrete‐time risk process allowing for delay in claim settlement, which introduces a certain type of dependence in the process. From martingale theory, an expression for the ultimate ruin probability is obtained, and Lundberg‐type inequalities are derived. The impact of delay in claim settlement is then investigated. To this end, a convex order comparison of the aggregate claim amounts is performed with the corresponding non‐delayed risk model, and numerical simulations are carried out with Belgian market data. Copyright © 2011 John Wiley & Sons, Ltd.

Suggested Citation

  • Julien Trufin & Hansjörg Albrecher & Michel Denuit, 2011. "Ruin problems under IBNR dynamics," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 27(6), pages 619-632, November.
    • Handle: RePEc:wly:apsmbi:v:27:y:2011:i:6:p:619-632
    DOI: 10.1002/asmb.875
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    Cited by:

    1. Lingjiong Zhu, 2023. "A delayed dual risk model," Papers 2301.06450, arXiv.org.
    2. Chehade, Abdallah & Savargaonkar, Mayuresh & Krivtsov, Vasiliy, 2022. "Conditional Gaussian mixture model for warranty claims forecasting," Reliability Engineering and System Safety, Elsevier, vol. 218(PB).
    3. He Liu & Zhenhua Bao, 2015. "On a Discrete Interaction Risk Model with Delayed Claims," JRFM, MDPI, vol. 8(4), pages 1-14, September.
    4. Filip Lindskog & Mario V. Wuthrich, 2024. "Claims processing and costs under capacity constraints," Papers 2409.09091, arXiv.org.

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