Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-26T05:33:02.491Z Has data issue: false hasContentIssue false
  • English
  • Français

FUNCTIONAL PROFILE TECHNIQUES FOR CLAIMS RESERVING

Published online by Cambridge University Press:  10 March 2022

Matúš Maciak Open the ORCID record for Matúš Maciak [Opens in a new window] ,
Ivan Mizera  and
Michal Pešta Open the ORCID record for Michal Pešta [Opens in a new window]
Matúš Maciak
Affiliation:
Faculty of Mathematics and Physics, Department of Probability and Mathematical Statistics, Charles University, Prague, Czech Republic E-mail: matus.maciak@mff.cuni.cz
Ivan Mizera
Affiliation:
Faculty of Science, Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada E-mail: imizera@ualberta.ca
Michal Pešta*
Affiliation:
Faculty of Mathematics and Physics, Department of Probability and Mathematical Statistics, Charles University, Prague, Czech Republic
*
E-mail: michal.pesta@mff.cuni.cz, pesta@karlin.mff.cuni.cz
Get access Rights & Permissions [Opens in a new window]

Abstract

One of the most fundamental tasks in non-life insurance, done on regular basis, is risk reserving assessment analysis, which amounts to predict stochastically the overall loss reserves to cover possible claims. The most common reserving methods are based on different parametric approaches using aggregated data structured in the run-off triangles. In this paper, we propose a rather non-parametric approach, which handles the underlying loss development triangles as functional profiles and predicts the claim reserve distribution through permutation bootstrap. Three competitive functional-based reserving techniques, each with slightly different scope, are presented; their theoretical and practical advantages – in particular, effortless implementation, robustness against outliers, and wide-range applicability – are discussed. Theoretical justifications of the methods are derived as well. An evaluation of the empirical performance of the designed methods and a full-scale comparison with standard (parametric) reserving techniques are carried on several hundreds of real run-off triangles against the known real loss outcomes. An important objective of the paper is also to promote the idea of natural usefulness of the functional reserving methods among the reserving practitioners.

Keywords

Claims reservingnon-life insurancereserving riskfunctional datadevelopment profilesconsistencypermutation bootstrap
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 52 , Issue 2 , May 2022 , pp. 449 - 482
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The International Actuarial Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Antonio, K. and Plat, R. (2014) Micro-level stochastic loss reserving for general insurance. Scandinavian Actuarial Journal, 2014(7), 649–669.CrossRefGoogle Scholar
Badescu, A.L., Chen, T., Lin, X.S. and Tang, D. (2019) A marked Cox model for the number of IBNR claims: Estimation and application. ASTIN Bulletin, 49(3), 709–739.CrossRefGoogle Scholar
Belyaev, Y.K. (1995) Bootstrap, Resampling and Mallows Metric. Lecture Notes 1, Institute of Mathematical Statistics, Umeå University.Google Scholar
Bornhuetter, R.L. and Ferguson, R.E. (1972) The actuary and IBNR. Proceedings of the Casualty Actuarial Society, LIX, 181–195.Google Scholar
Bühlmann, H. (1983) Estimation of IBNR reserves by the methods chain ladder, Cape Cod and complementary loss ratio. International Summer School 1983 (unpublished).Google Scholar
Clark, D.R. (2003) LDF curve-fitting and stochastic reserving: A maximum likelihood approach. Casualty Actuarial Society, E-Forum, Fall 2003, 41–92.Google Scholar
Clark, D.R. (2016) Introduction to Bayesian loss development. Casualty Actuarial Society, E-Forum, Summer 2016, 319–342.Google Scholar
Delaigle, A. and Hall, P. (2013) Classification using censored functional data. Journal of the American Statistical Association, 108(504), 1269–1283.CrossRefGoogle Scholar
Delaigle, A. and Hall, P. (2016) Approximating fragmented functional data by segments of Markov chains. Biometrika, 103(4), 779–799.CrossRefGoogle Scholar
Delong, L., Lindholm, M. and Wüthrich, M.V. (2021) Collective reserving using individual claims data. Scandinavian Actuarial Journal, 1–28. https://doi.org/10.1080/03461238.2021.1921836.CrossRefGoogle Scholar
Efron, B. and Tibshirani, R.J. (1993) An Introduction to the Bootstrap. London, UK: Chapman and Hall/CRC.CrossRefGoogle Scholar
England, P.D. and Verrall, R.J. (1999) Analytic and bootstrap estimates of prediction errors in claims reserving. Insurance: Mathematics and Economics, 25(3), 281–293.Google Scholar
England, P.D. and Verrall, R.J. (2001) A flexible framework for stochastic claims reserving. Proceedings of the Casualty Actuarial Society, LXXXVIII(168), 1–38.Google Scholar
England, P.D. and Verrall, R.J. (2002) Stochastic claims reserving in general insurance (with discussion). British Actuarial Journal, 8(3), 443–518.CrossRefGoogle Scholar
Gerthofer, M. and Pešta, M. (2017) Stochastic claims reserving in insurance using random effects. Insurance: Mathematics and Economics, 26(5), 542–560.Google Scholar
Godecharle, E. and Antonio, K. (2015) Reserving by conditioning on markers of individual claims: A case study using historical simulation. North American Actuarial Journal, 19(4), 273–288.CrossRefGoogle Scholar
Hesselager, O. (1994) A Markov model for loss reserving. ASTIN Bulletin, 24(2), 183–193.CrossRefGoogle Scholar
Huang, J., Qiu, C. and Wu, X. (2015) Stochastic loss reserving in discrete time: Individual vs. aggregate data models. Communications in Statistics – Theory and Methods, 44(10), 2180–2206.CrossRefGoogle Scholar
Huang, J., Wu, X. and Zhou, X. (2016) Asymptotic behaviors of stochastic reserving: Aggregate versus individual models. European Journal of Operational Research, 249(2), 657–666.CrossRefGoogle Scholar
Hudecová, š. and Pešta, M. (2013) Modeling dependencies in claims reserving with GEE. Insurance: Mathematics and Economics, 53(3), 786–794.Google Scholar
Hürlimann, W. (2009) Credible loss ratio claims reserves: the Benktander, Neuhaus and Mack methods revisited. ASTIN Bulletin, 39(1), 81–99.CrossRefGoogle Scholar
Jewell, W. (1989) Predicting IBNYR events and delays, part I continuous time. ASTIN Bulletin, 19, 25–56.CrossRefGoogle Scholar
Jewell, W. (1990) Predicting IBNYR events and delays, part II discrete time. ASTIN Bulletin, 20, 93–111.CrossRefGoogle Scholar
Kim, M.-S., Park, H.-J, Hwang, C. and Shi, J.-Y. (2008) Claims reserving via kernel machine. Journal of the Korean Data and Information Science Society, 19(4), 1419–1427.Google Scholar
Kremer, E. (1984) A class of autoregressive models for predicting the final claims amount. Insurance: Mathematics and Economics, 3(2), 111–119.Google Scholar
Maciak, M., Okhrin, O. and Pešta, M. (2021) Infinitely stochastic micro reserving. Insurance: Mathematics and Economics, 100(2021), 30–58.Google Scholar
Mack, T. (1993) Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin, 23(2), 213–225.CrossRefGoogle Scholar
Mack, T. (1994) Which stochastic model is underlying the chain ladder model? Insurance: Mathematics and Economics, 15, 133–138.Google Scholar
Mack, T. (1999) The standard error of chain ladder reserve estimates: Recursive calculation and inclusion of a tail factor. ASTIN Bulletin, 29(3), 361–366.CrossRefGoogle Scholar
Mack, T. and Venter, G. (2000) A comparison of stochastic models that reproduce chain ladder reserve estimates. Insurance: Mathematics and Economics, 26(1), 101–107.Google Scholar
McCullagh, P. and Nelder, J.A. (1989) Generalized Linear Models (2nd ed.). Boca Raton, FL: Chapman & Hall.CrossRefGoogle Scholar
Meyers, G. and Shi, P. (2011a) The retrospective testing of stochastic loss reserve methods. CAS E-Forum, Summer 2011, 1–37.Google Scholar
Meyers, G.G. and Shi, P. (2011b) Loss reserving data pulled from NAIC Schedule P. Online; Available from https://www.casact.org/publications-research/research/research-resources/loss-reserving-data-pulled-naic-schedule-p; Updated September 01, 2011; Accessed June 10, 2014.Google Scholar
Murphy, D.M. (1994) Unbiased loss development factors. CAS Forum, LXXXI(Vol. 1), 154–222.Google Scholar
Pesarin, F. and Salmaso, L. (2010) Permutation Tests for Complex Data: Theory, Applications and Software. New York, NY: Wiley.CrossRefGoogle Scholar
Pešta, M. and Hudecová, š. (2012) Asymptotic consistency and inconsistency of the chain ladder. Insurance: Mathematics and Economics, 51(2), 472–479.Google Scholar
Pešta, M. and Okhrin, O. (2014) Conditional least squares and copulae in claims reserving for a single line of business. Insurance: Mathematics and Economics, 56(1), 28–37.Google Scholar
Pigeon, M., Antonio, K. and Denuit, M. (2014) Individual loss reserving using paid-incurred data. Insurance: Mathematics and Economics, 58, 121–131.Google Scholar
Pinheiro, P.J.R., Andradee Silva, J.M. and De Lourdes Centeno, M. (2003) Bootstrap methodology in claim reserving. Journal of Risk and Insurance, 70(4), 701–714.CrossRefGoogle Scholar
Popescu, R. and Suciu, D. (2020) Glancing back. The Actuary, 2020(July), 20–22.Google Scholar
Renshaw, A.E. and Verrall, R.J. (1998) A stochastic model underlying the chain-ladder technique. British Actuarial Journal, 4, 903–923.CrossRefGoogle Scholar
Taylor, G. (2000) Loss Reserving: An Actuarial Perspective. Boston, MA: Kluwer Academic Publishers.CrossRefGoogle Scholar
Verdonck, T. and Debruyne, M. (2011) The influence of individual claims on the chain-ladder estimates: Analysis and diagnostic tool. Insurance: Mathematics and Economics, 48(1), 85–98.Google Scholar
Verrall, R., Nielsen, J.P. and Jessen, A.H. (2010) Prediction of RBNS and IBNR claims using claim amounts and claim counts. ASTIN Bulletin, 40(2), 871–887.Google Scholar
Verrall, R.J. (1996). Claims reserving and generalised additive models. Insurance: Mathematics and Economics, 19(1), 31–43.Google Scholar
Wahl, F., Lindholm, M. and Verrall, R. (2019) The collective reserving model. Insurance: Mathematics and Economics, 87, 34–50.Google Scholar
Wüthrich, M.V. (2018) Machine learning in individual claims reserving. Scandinavian Actuarial Journal, 2018(6), 465–480.CrossRefGoogle Scholar
Wüthrich, M.V. and Merz, M. (2008) Stochastic Claims Reserving Methods in Insurance . Wiley Finance Series. Hoboken, NJ: John Wiley & Sons.Google Scholar
Zhao, X. and Zhou, X. (2010) Applying copula models to individual claim loss reserving methods. Insurance: Mathematics and Economics, 46, 290–299.Google Scholar
Supplementary material: PDF

Maciak et al. supplementary material

Maciak et al. supplementary material

Download Maciak et al. supplementary material(PDF)
PDF 391.6 KB