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Modeling the number of hidden events subject to observation delay

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  • Jonas Crevecoeur
  • Katrien Antonio
  • Roel Verbelen

Abstract

This paper considers the problem of predicting the number of events that have occurred in the past, but which are not yet observed due to a delay. Such delayed events are relevant in predicting the future cost of warranties, pricing maintenance contracts, determining the number of unreported claims in insurance and in modeling the outbreak of diseases. Disregarding these unobserved events results in a systematic underestimation of the event occurrence process. Our approach puts emphasis on modeling the time between the occurrence and observation of the event, the so-called observation delay. We propose a granular model for the heterogeneity in this observation delay based on the occurrence day of the event and on calendar day effects in the observation process, such as weekday and holiday effects. We illustrate this approach on a European general liability insurance data set where the occurrence of an accident is reported to the insurer with delay.

Suggested Citation

  • Jonas Crevecoeur & Katrien Antonio & Roel Verbelen, 2018. "Modeling the number of hidden events subject to observation delay," Papers 1801.02935, arXiv.org, revised Mar 2019.
    • Handle: RePEc:arx:papers:1801.02935
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    References listed on IDEAS

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    1. Wang, Wenbin, 2010. "A model for maintenance service contract design, negotiation and optimization," European Journal of Operational Research, Elsevier, vol. 201(1), pages 239-246, February.
    2. Berrade, M.D. & Scarf, P.A. & Cavalcante, C.A.V., 2018. "Conditional inspection and maintenance of a system with two interacting components," European Journal of Operational Research, Elsevier, vol. 268(2), pages 533-544.
    3. Mack, Thomas, 1999. "The Standard Error of Chain Ladder Reserve Estimates: Recursive Calculation and Inclusion of a Tail Factor," ASTIN Bulletin, Cambridge University Press, vol. 29(2), pages 361-366, November.
    4. Pigeon, Mathieu & Antonio, Katrien & Denuit, Michel, 2014. "Individual loss reserving using paid–incurred data," LIDAM Reprints ISBA 2014024, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Pigeon, Mathieu & Antonio, Katrien & Denuit, Michel, 2013. "Individual Loss Reserving With The Multivariate Skew Normal Framework," ASTIN Bulletin, Cambridge University Press, vol. 43(3), pages 399-428, September.
    6. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(3), pages 443-518, August.
    7. Haastrup, Svend & Arjas, Elja, 1996. "Claims Reserving in Continuous Time; A Nonparametric Bayesian Approach," ASTIN Bulletin, Cambridge University Press, vol. 26(2), pages 139-164, November.
    8. Badescu, Andrei L. & Lin, X. Sheldon & Tang, Dameng, 2016. "A marked Cox model for the number of IBNR claims: Theory," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 29-37.
    9. Huang, Jinlong & Wu, Xianyi & Zhou, Xian, 2016. "Asymptotic behaviors of stochastic reserving: Aggregate versus individual models," European Journal of Operational Research, Elsevier, vol. 249(2), pages 657-666.
    10. Angela Noufaily & Paddy Farrington & Paul Garthwaite & Doyo Gragn Enki & Nick Andrews & Andre Charlett, 2016. "Detection of Infectious Disease Outbreaks From Laboratory Data With Reporting Delays," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 488-499, April.
    11. Huang, Jinlong & Qiu, Chunjuan & Wu, Xianyi & Zhou, Xian, 2015. "An individual loss reserving model with independent reporting and settlement," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 232-245.
    12. Wang, W., 1997. "Subjective estimation of the delay time distribution in maintenance modelling," European Journal of Operational Research, Elsevier, vol. 99(3), pages 516-529, June.
    13. Pigeon, Mathieu & Antonio, Katrien & Denuit, Michel, 2014. "Individual loss reserving using paid–incurred data," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 121-131.
    14. Marco Bonetti & Pasquale Cirillo & Paola Musile Tanzi & Elisabetta Trinchero, 2016. "An Analysis of the Number of Medical Malpractice Claims and Their Amounts," PLOS ONE, Public Library of Science, vol. 11(4), pages 1-30, April.
    15. Mack, Thomas, 1993. "Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 213-225, November.
    16. Mario V. Wuthrich & Michael Merz, 2015. "Stochastic Claims Reserving Manual: Advances in Dynamic Modeling," Swiss Finance Institute Research Paper Series 15-34, Swiss Finance Institute.
    17. D. Kuang & B. Nielsen & J. P. Nielsen, 2008. "Identification of the age-period-cohort model and the extended chain-ladder model," Biometrika, Biometrika Trust, vol. 95(4), pages 979-986.
    18. Els Godecharle & Katrien Antonio, 2015. "Reserving by Conditioning on Markers of Individual Claims: A Case Study Using Historical Simulation," North American Actuarial Journal, Taylor & Francis Journals, vol. 19(4), pages 273-288, October.
    19. Norberg, Ragnar, 1993. "Prediction of Outstanding Liabilities in Non-Life Insurance1," ASTIN Bulletin, Cambridge University Press, vol. 23(1), pages 95-115, May.
    20. Tim Verdonck & Martine Van Wouwe & Jan Dhaene, 2009. "A Robustification of the Chain-Ladder Method," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(2), pages 280-298.
    21. Mortenson, Michael J. & Doherty, Neil F. & Robinson, Stewart, 2015. "Operational research from Taylorism to Terabytes: A research agenda for the analytics age," European Journal of Operational Research, Elsevier, vol. 241(3), pages 583-595.
    22. S Apeland & P A Scarf, 2003. "A fully subjective approach to capital equipment replacement," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(4), pages 371-378, April.
    23. Apeland, S. & Scarf, P. A., 2003. "A fully subjective approach to modelling inspection maintenance," European Journal of Operational Research, Elsevier, vol. 148(2), pages 410-425, July.
    24. Avanzi, Benjamin & Wong, Bernard & Yang, Xinda, 2016. "A micro-level claim count model with overdispersion and reporting delays," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 1-14.
    25. Jewell, William S., 1990. "Predicting IBNYR Events and Delays II. Discrete Time," ASTIN Bulletin, Cambridge University Press, vol. 20(1), pages 93-111, April.
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    Cited by:

    1. Crevecoeur, Jonas & Robben, Jens & Antonio, Katrien, 2022. "A hierarchical reserving model for reported non-life insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 104(C), pages 158-184.
    2. Avanzi, Benjamin & Taylor, Greg & Wong, Bernard & Xian, Alan, 2021. "Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework," European Journal of Operational Research, Elsevier, vol. 290(1), pages 177-195.
    3. Benjamin Avanzi & Greg Taylor & Bernard Wong & Alan Xian, 2020. "Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework," Papers 2003.13888, arXiv.org, revised May 2020.
    4. Stephan M. Bischofberger, 2020. "In-Sample Hazard Forecasting Based on Survival Models with Operational Time," Risks, MDPI, vol. 8(1), pages 1-17, January.
    5. Chehade, Abdallah & Savargaonkar, Mayuresh & Krivtsov, Vasiliy, 2022. "Conditional Gaussian mixture model for warranty claims forecasting," Reliability Engineering and System Safety, Elsevier, vol. 218(PB).
    6. Oliver Lunding Sandqvist, 2023. "A multistate approach to disability insurance reserving with information delays," Papers 2312.14324, arXiv.org.

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