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Market-based insurance ratemaking: Application to pet insurance

Part of: Applications Mathematical finance Parametric inference

Published online by Cambridge University Press:  11 April 2025

Pierre-Olivier Goffard Open the ORCID record for Pierre-Olivier Goffard [Opens in a new window] ,
Pierrick Piette  and
Gareth W. Peters
Pierre-Olivier Goffard*
Affiliation:
Institut de Recherche Mathématique Avancée, Université de Strasbourg, Strasbourg, France
Pierrick Piette
Affiliation:
Laboratoire SAF EA2429, Institut de Science Financière et d’Assurances (ISFA), Univ Lyon, Université Claude Bernard Lyon 1, F-69366, Lyon, France Hestialytics, Paris, France
Gareth W. Peters
Affiliation:
Department of Statistics and Applied Probability, University of California Santa Barbara, Santa Barbara, CA 93106-3110, USA
*
*Corresponding author: Pierre-Olivier Goffard; Email: pierre.olivier.goffard@gmail.com
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Abstract

This paper introduces a method for pricing insurance policies using market data. The approach is designed for scenarios in which the insurance company seeks to enter a new market, in our case: pet insurance, lacking historical data. The methodology involves an iterative two-step process. First, a suitable parameter is proposed to characterize the underlying risk. Second, the resulting pure premium is linked to the observed commercial premium using an isotonic regression model. To validate the method, comprehensive testing is conducted on synthetic data, followed by its application to a dataset of actual pet insurance rates. To facilitate practical implementation, we have developed an R package called IsoPriceR. By addressing the challenge of pricing insurance policies in the absence of historical data, this method helps enhance pricing strategies in emerging markets.

Keywords

Insurance pricingBayesian inferenceapproximate Bayesian computationisotonic regression

MSC classification

Primary: 62P05: Applications to actuarial sciences and financial mathematics
Secondary: 91G70: Statistical methods, econometrics 62F15: Bayesian inference

Information

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 55 , Issue 2 , May 2025 , pp. 263 - 286
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The International Actuarial Association

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References

Antonio, K. and Valdez, E.A. (2011) Statistical concepts of a priori and a posteriori risk classification in insurance. AStA Advances in Statistical Analysis, 96 (2), 187–224. ISSN 1863-818X. doi: 10.1007/s10182-011-0152-7.CrossRefGoogle Scholar
Barber, S., Voss, J. and Webster, M. (2015) The rate of convergence for approximate Bayesian computation. Electronic Journal of Statistics, 9(1). ISSN 1935-7524. doi: 10.1214/15-ejs988.CrossRefGoogle Scholar
Barlow, R.E., Brunk, H.D., Bartholomew, D.J. and Bremner, J.M. (1972) Statistical inference under order restrictions.(the theory and application of isotonic regression).Google Scholar
Beaumont, M.A., Cornuet, J.-M., Marin, J.-M. and Robert, C.P. (2009) Adaptive approximate Bayesian computation. Biometrika, 96(4), 983–990.10.1093/biomet/asp052CrossRefGoogle Scholar
Blier-Wong, C., Cossette, H., Lamontagne, L. and Marceau, E. (2020) Machine learning in p&c insurance: A review for pricing and reserving. Risks, 9(1), 4. doi: 10.3390/risks9010004.CrossRefGoogle Scholar
Dean, T.A., Singh, S.S., Jasra, A. and Peters, G.W. (2014) Parameter estimation for hidden Markov models with intractable likelihoods. Scandinavian Journal of Statistics, 41(4), 970–987.10.1111/sjos.12077CrossRefGoogle Scholar
Del Moral, P., Doucet, A. and Jasra, A. (2006) Sequential Monte Carlo samplers. Journal of the Royal Statistical Society Series B: Statistical Methodology, 68(3), 411–436. ISSN 1467-9868. doi: 10.1111/j.1467-9868.2006.00553.x.CrossRefGoogle Scholar
Del Moral, P., Doucet, A. and Jasra, A. (2012a) An adaptive sequential Monte Carlo method for approximate Bayesian computation. Statistics and Computing, 22(5), 1009–1020.10.1007/s11222-011-9271-yCrossRefGoogle Scholar
Del Moral, P., Doucet, A. and Jasra, A. (2012b) On adaptive resampling strategies for sequential monte carlo methods. Bernoulli, 18(1). ISSN 1350-7265. doi: 10.3150/10-bej335.CrossRefGoogle Scholar
Dickson, D. (2005) Principles of premium calculation. In Insurance Risk and Ruin, pp. 38–51. Cambridge University Press. doi: 10.1017/cbo9780511624155.004.CrossRefGoogle Scholar
Goffard, P.-O. and Laub, P.J. (2021) Approximate Bayesian computations to fit and compare insurance loss models. Insurance: Mathematics and Economics, 100, 350–371. doi: 10.1016/j.insmatheco.2021.06.002.Google Scholar
Gourieroux, C., Monfort, A. and Renault, E. (1993) Indirect inference. Journal of Applied Econometrics, 8(S1), S85–S118. doi: 10.1002/jae.3950080507.CrossRefGoogle Scholar
Hansen, L.P. (1982) Large sample properties of generalized method of moments estimators. Econometrica, 50(4), 1029. ISSN 0012-9682. doi: 10.2307/1912775.CrossRefGoogle Scholar
Kong, A., Liu, J.S. and Wong, W.H. (1994) Sequential imputations and Bayesian missing data problems. Journal of the American Statistical Association, 89 (425), 278–288. doi: 10.1080/01621459.1994.10476469.CrossRefGoogle Scholar
Luss, R. and Rosset, S. (2014) Generalized isotonic regression. Journal of Computational and Graphical Statistics, 23 (1), 192–210.10.1080/10618600.2012.741550CrossRefGoogle Scholar
Peters, G. and Sisson, S. (2006) Bayesian inference, Monte Carlo sampling and operational risk. Peters GW and Sisson SA (2006) “Bayesian Inference, Monte Carlo Sampling and Operational Risk”. Journal of Operational Risk, 1(3).Google Scholar
Peters, G.W., Wüthrich, M.V. and Shevchenko, P.V. (2010) Chain ladder method: Bayesian bootstrap versus classical bootstrap. Insurance: Mathematics and Economics, 47 (1), 36–51.Google Scholar
Renshaw, A.E. (1994) Modelling the claims process in the presence of covariates. ASTIN Bulletin, 24(2), 265–285. doi: 10.2143/AST.24.2.2005070.CrossRefGoogle Scholar
Rubio, F.J. and Johansen, A.M. (2013) A simple approach to maximum intractable likelihood estimation. Electronic Journal of Statistics, 7, 1632–1654.10.1214/13-EJS819CrossRefGoogle Scholar
Sasabuchi, S., Inutsuka, M. and Kulatunga, D.D.S. (1983) A multivariate version of isotonic regression. Biometrika, 70(2), 465–472. ISSN 1464-3510. doi: 10.1093/biomet/70.2.465.CrossRefGoogle Scholar
Sisson, S.A., Fan, Y. and Beaumont, M. (2018) Handbook of Approximate Bayesian Computation. New York: Chapman and Hall/CRC.10.1201/9781315117195CrossRefGoogle Scholar
Wüthrich, M.V. and Ziegel, J. (2023) Isotonic recalibration under a low signal-to-noise ratio.10.1080/03461238.2023.2246743CrossRefGoogle Scholar
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