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A note on discounted compound renewal sums under dependency

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  • Woo, Jae-Kyung
  • Cheung, Eric C.K.

Abstract

The paper considers a renewal risk process in which a given inter-arrival time possibly has an impact on the size of the resulting claim. Under a fairly general dependency structure which contains various well-known examples in the literature as special cases, recursive formulas for the moments of the discounted aggregate claims are derived using the techniques in Léveillé and Garrido (2001b). Simplifications arise in the case of a dependent renewal risk process under ‘Erlang weights’. Numerical examples are given towards the end to illustrate the impact of dependency on the discounted aggregate claims.

Suggested Citation

  • Woo, Jae-Kyung & Cheung, Eric C.K., 2013. "A note on discounted compound renewal sums under dependency," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 170-179.
    • Handle: RePEc:eee:insuma:v:52:y:2013:i:2:p:170-179
    DOI: 10.1016/j.insmatheco.2012.11.005
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    References listed on IDEAS

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    Cited by:

    1. Ghislain Léveillé & Ilie-Radu Mitric & Victor Côté, 2018. "Effects of the Age Process on Aggregate Discounted Claims," Risks, MDPI, vol. 6(4), pages 1-17, September.
    2. Landriault, David & Willmot, Gordon E. & Xu, Di, 2014. "On the analysis of time dependent claims in a class of birth process claim count models," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 168-173.
    3. Castañer, A. & Claramunt, M.M. & Lefèvre, C. & Loisel, S., 2015. "Discrete Schur-constant models," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 343-362.
    4. Siti Norafidah Mohd Ramli & Jiwook Jang, 2014. "Neumann Series on the Recursive Moments of Copula-Dependent Aggregate Discounted Claims," Risks, MDPI, vol. 2(2), pages 1-16, May.
    5. Landy Rabehasaina & Jae-Kyung Woo, 2018. "On a multivariate renewal-reward process involving time delays and discounting: applications to IBNR processes and infinite server queues," Queueing Systems: Theory and Applications, Springer, vol. 90(3), pages 307-350, December.
    6. Cheung, Eric C.K. & Ni, Weihong & Oh, Rosy & Woo, Jae-Kyung, 2021. "Bayesian credibility under a bivariate prior on the frequency and the severity of claims," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 274-295.
    7. Shuanming Li & Yi Lu, 2018. "On the Moments and the Distribution of Aggregate Discounted Claims in a Markovian Environment," Risks, MDPI, vol. 6(2), pages 1-16, May.
    8. Castañer, A. & Claramunt, M.M. & Lefèvre, C. & Loisel, S., 2015. "Discrete Schur-constant models," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 343-362.
    9. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.
    10. Woo, Jae-Kyung, 2016. "On multivariate discounted compound renewal sums with time-dependent claims in the presence of reporting/payment delays," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 354-363.
    11. Sharifah Farah Syed Yusoff Alhabshi & Zamira Hasanah Zamzuri & Siti Norafidah Mohd Ramli, 2021. "Monte Carlo Simulation of the Moments of a Copula-Dependent Risk Process with Weibull Interwaiting Time," Risks, MDPI, vol. 9(6), pages 1-21, June.

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