To calculate claims reserves more frequently than the usual yearly periods for which ultimate loss development factors are available, it is necessary to perform an extrapolation prior to the time marking the end of the first development year and an interpolation for each successive development year. A simple power law extrapolation – interpolation method is developed and illustrated for monthly and quarterly sub-periods.
| Published in | Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 1) |
| DOI | 10.11648/j.sjams.20150301.12 |
| Page(s) | 6-13 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Claims Reserving, IBNR Reserve, Loss Development Factors, Interpolation, Extrapolation, Power Law
| [1] | A. Boulter and D. Grubbs, “Late claims in reinsurance”, Publication Swiss Reinsurance Company, URL: http://www.swissre.com, 2000. |
| [2] | P. De Jong, “Modeling dependence between loss triangles”, North American Actuarial Journal 16(1), 74-86, 2012. |
| [3] | M. Eling, D. Diers, M. Linde and C. Kraus, “The multi-year non-life insurance risk”, Working papers on risk management and insurance no. 96, Institute of Insurance Economics, University of St. Gallen, November 2011. |
| [4] | P. Gigante, L. Picech and L Sigalotti, “Prediction error for credible claims reserves: an h-likelihood approach”, European Actuarial Journal 3(2), 453-470, 2013. |
| [5] | S. Happ, “Stochastic claims reserving under consideration of various different sources of information”, Dissertation, University Hamburg. |
| [6] | Huang, J. and X. Wu, “Stochastic claims reserving in general insurance: models and methodologies”, 2012 China International Conference on Insurance and Risk Management, Qingdao, 2012. |
| [7] | W. Hürlimann, “Modelling non-life insurance risk for Solvency II in a reinsurance context”, Life & Pensions Magazine, January issue, 35-40, 2010. |
| [8] | W. Hürlimann, “A Gamma IBNR claims reserving model with dependent development periods”, Proc. 37th Internat. ASTIN Colloquium, Orlando, 2007. |
| [9] | W. Hürlimann, “Credible loss ratio claims reserves – the Benktander, Neuhaus and Mack methods revisited”, ASTIN Bulletin 39(1), 81-100, 2009. |
| [10] | W. Hürlimann, “Random loss development factor curves and stochastic claims reserving”, JP Journal of Fundamental and Applied Statistics 1(1), 49-62, 2011. |
| [11] | T. Mack, “Credible claims reserve: the Benktander method” , ASTIN Bulletin 30(2), 333-347, 2000. |
| [12] | M. Merz and M.V. Wüthrich, “Modelling the claims development result for solvency purposes”, 38th ASTIN Colloquium, Manchester, 2008. |
| [13] | M. Pirra, S. Forte and M. Ialenti, “Implementing a Solvency II internal model : Bayesian stochasting reserving and parameter estimation”, 40th ASTIN Colloquium, Madrid, 2011. |
| [14] | M. Radtke and K.D. Schmidt, “Handbuch zur Schaden- reservierung”, 2nd ed., Verlag Versicherungswirtschaft, Karlsruhe, 2012. |
| [15] | L. Regis, “A Bayesian copula model for stochastic claims reserving”, working paper no. 227, Collegio Carlo Alberto, 2011. |
| [16] | I. Robbin, D. Homer, “Analysis of loss development patterns using infinitely decomposable percent of ultimate curves”, 1988 Discussion Papers on Evaluating Insurance Company Liabilities, Casual Actuarial Society, 503-538, URL: http://www.casact.org/pubs/dpp/dpp88/88dpp501.pdf |
| [17] | R. Salzmann, “Stochastic claims reserving and solvency”, Diss. ETH no. 20406, Zürich, 2012. |
| [18] | R. Salzmann, M.V. Wüthrich, “Modeling accounting year dependence in runoff triangles”, European Actuarial Journal 2(2), 227-242, 2012. |
| [19] | N. Savelli and G.P. Clemente, “Stochastic claims reserving based on CRM for Solvency II purposes”, 40th ASTIN Colloquium, Madrid, 2011. |
| [20] | M. Schiegl, “A three dimensional stochastic model for claim reserving”, preprint, arXiv: 1009.4146 [q-fin.RM], 2010. |
| [21] | K.D. Schmidt, “A bibliography on loss reserving”, Technische Universität Dresden, update November 17, 2013. |
| [22] | R.E. Sherman, “Extrapolating, smoothing and interpolating development factors”, Proceedings of the Casualty Actuarial Society LXXI, 122-199, 1984. |
| [23] | D. Subotzuky and J. Mazur, “How do you square the triangle”, Reinsurance Magazine, Sept. 2006. |
| [24] | M.V. Wüthrich and M. Merz, Stochastic Claims Reserving Methods in Insurance, J. Wiley, New York, 2008. |
APA Style
Werner Hürlimann. (2015). A Power Law Extrapolation – Interpolation Method for IBNR Claims Reserving. Science Journal of Applied Mathematics and Statistics, 3(1), 6-13. https://doi.org/10.11648/j.sjams.20150301.12
ACS Style
Werner Hürlimann. A Power Law Extrapolation – Interpolation Method for IBNR Claims Reserving. Sci. J. Appl. Math. Stat. 2015, 3(1), 6-13. doi: 10.11648/j.sjams.20150301.12
AMA Style
Werner Hürlimann. A Power Law Extrapolation – Interpolation Method for IBNR Claims Reserving. Sci J Appl Math Stat. 2015;3(1):6-13. doi: 10.11648/j.sjams.20150301.12
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.sjams.20150301.12,
author = {Werner Hürlimann},
title = {A Power Law Extrapolation – Interpolation Method for IBNR Claims Reserving},
journal = {Science Journal of Applied Mathematics and Statistics},
volume = {3},
number = {1},
pages = {6-13},
doi = {10.11648/j.sjams.20150301.12},
url = {https://doi.org/10.11648/j.sjams.20150301.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150301.12},
abstract = {To calculate claims reserves more frequently than the usual yearly periods for which ultimate loss development factors are available, it is necessary to perform an extrapolation prior to the time marking the end of the first development year and an interpolation for each successive development year. A simple power law extrapolation – interpolation method is developed and illustrated for monthly and quarterly sub-periods.},
year = {2015}
}
TY - JOUR T1 - A Power Law Extrapolation – Interpolation Method for IBNR Claims Reserving AU - Werner Hürlimann Y1 - 2015/02/02 PY - 2015 N1 - https://doi.org/10.11648/j.sjams.20150301.12 DO - 10.11648/j.sjams.20150301.12 T2 - Science Journal of Applied Mathematics and Statistics JF - Science Journal of Applied Mathematics and Statistics JO - Science Journal of Applied Mathematics and Statistics SP - 6 EP - 13 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20150301.12 AB - To calculate claims reserves more frequently than the usual yearly periods for which ultimate loss development factors are available, it is necessary to perform an extrapolation prior to the time marking the end of the first development year and an interpolation for each successive development year. A simple power law extrapolation – interpolation method is developed and illustrated for monthly and quarterly sub-periods. VL - 3 IS - 1 ER -
Information
Email: