Empirical Analysis of Claims Development Trapezoids following Benford’s Law
Vol 3, Issue 1, 2020
VIEWS - 3355 (Abstract) 2663 (PDF)
Abstract
In this paper we make an empirical analysis of a wide range of claims development trapezoids following Benford’s law. In particular we determine Benfors’s law for different characteristic factors depending on claims development triangles/trapezoids. These characteristic factors are the cumulative claims payments, the incremental claims payments and the individual development factors. For each characteristic factor hypothesis testing is done for verifying/rejecting Benford’s law.
Keywords
Full Text:
PDFReferences
1. Arnold, T. A. & Emerson, J. W. (2011): Nonparametric Goodness-of-Fit Tests for Discrete Null Distributions. The R Journal, 3(2): 34–39 (cit. on p. 8).
2. Benford, F. (1938): The Law of Anomalous Numbers. Proceedings of the American Philosophical Society, 78(4): 551–572 (cit. on pp. 1, 5).
3. Berger, A. & Hill, T. P. (2011): A basic theory of Benford’s Law. Probability Surveys, 8: 1–126 (cit. on p. 6).
4. Diaconis, P. (1977): The Distribution of Leading Digits and Uniform Distribution Mod 1. The Annals of Probability, 5(1): 72–81 (cit. on p. 6).
5. Diekmann, A. & Jann, B. (2010): Benford’s Law and Fraud Detection: Facts and Legends. German Economic Review, 11(3): 397–401 (cit. on p. 2).
6. Durtschi, C.; Hillison, W. & Pacini, C. (2004): The Effective Use of Benford’s Law to Assist in Detecting Fraud in Accounting Data. Journal of Forensic Accounting, 5(1): 17–34 (cit. on p. 2).
7. England, P. D. & Verrall, R. J. (2001): A flexible framework for stochastic claims reserving. Proceedings of the Casualty Actuarial Society. Vol. 88. 1: 1–38 (cit. on p. 2).
8.
9. England, P. D. & Verrall, R. J. (1999): Analytic and bootstrap estimates of prediction errors in claims reserving. Insurance: Mathematics and Economics, 25(3): 281–293 (cit. on p. 2).
10. Gleser, L. J. (1985): Exact Power of Goodness-of-Fit Tests of Kolmogorov Type for Discontinuous Distributions. Journal of the American Statistical Association, 80(392): 954–958 (cit. on p. 8).
11. Govindarajulu, Z. (2007): Nonparametric Inference. World Scientific (cit. on p. 2).
12. Heberle, J.; Huergo, L. & Merz, M. (2010): Bootstrapping the Chain-Ladder-Method of Several Correlated Run-Off Portfolios. Zeitschrift für die gesamte Versicherungswissenschaft, 98(5): 541–564 (cit. on p. 2).
13. Mack, T. (1993): Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin, 23(2): 213–225 (cit. on p. 2).
14. Merz, M. & Wüthrich, M. V. (2007): Prediction error of the expected claims development
15. result in the chain ladder method. Bulletin of Swiss Association of Actuaries, 1: 117–137 (cit. on p. 2). [14] Pinheiro, P. J. R.; Andrade e Silva, J. M. & de Lourdes Centeno, M. (2003): Bootstrap Methodology in Claim Reserving. Journal of Risk and Insurance, 70(4): 701–714 (cit. on p. 2).
16. R Development Core Team (2014): R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing (cit. on p. 8).
DOI: https://doi.org/10.24294/fsj.v3i1.420
Refbacks
- There are currently no refbacks.
Copyright (c) 2020 Jochen Heberle, Tobias Gummersbach
License URL: https://creativecommons.org/licenses/by-nc/4.0
This site is licensed under a Creative Commons Attribution 4.0 International License.