Number of Accidents or Number of Claims? An Approach with Zero‐Inflated Poisson Models for Panel Data
Abstract
The hunger for bonus is a well‐known phenomenon in insurance, meaning that the insured does not report all of his accidents to save bonus on his next year's premium. In this article, we assume that the number of accidents is based on a Poisson distribution but that the number of claims is generated by censorship of this Poisson distribution. Then, we present new models for panel count data based on the zero‐inflated Poisson distribution. From the claims distributions, we propose an approximation of the accident distribution, which can provide insight into the behavior of insureds. A numerical illustration based on the reported claims of a Spanish insurance company is included to support this discussion.
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Cites
Bonus-Malus Systems in Automobile Insurance
Lemaire, J. (1995) · Huebner International Series on Risk, Insurance, and Economic Security · doi:10.1007/978-94-011-0631-3 · Cited by 325 · cited 1× · see citing works
“In most of the bonus-malus schemes throughout the world (see Lemaire (1995) for an overview), a reported claim causes an increase in the premium for the following years.”
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Research works printed but not linked: 20
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The Use of Telematics Devices to Improve Automobile Insurance Rates
Guillen, M., Nielsen, J. P., Ayuso, M., & Pérez‐Marín, A. M. (2019) · Risk Analysis · doi:10.1111/risa.13172 · Cited by 98 · see citing works
Self-citation
- Authors
- Boucher, J., Denuit, M., & Guillen, M.
- Affiliations
- Université du Québec à Montréal (CA)
- UCLouvain (BE)
- ORCID
- Denuit, Michel
- Venue
- Journal of Risk and Insurance
- Publisher
- Wiley
- Published
- 2009-11-06
- Volume
- 76
- Issue
- 4
- Pages
- 821-846
- ISSN
- 0022-4367 (ISSN-L)
- 1539-6975
- OpenAlex
- W2025329530
- Cited by
- 98
- References
- 1
- Citations by year
- 2026: 5 · 2025: 5 · 2024: 5 · 2023: 8 · 2022: 6 · 2021: 5 · 2020: 6 · 2019: 7 · 2018: 11 · 2017: 4 · 2016: 3 · 2015: 3 · 2014: 6 · 2013: 4 · 2012: 3
- FWCI
- 8.14
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Risk & Insurance (publishedVersion)
- Archipel (Université du Québec à Montréal) (acceptedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- DIAL (Catholic University of Leuven) (submittedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Probability and Risk Models
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Insurance and Financial Risk Management
- Keywords
- zero-inflated Poisson distribution, panel count data, insurance claims, underreporting of accidents, censorship, accident distribution, premium discounts
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