Reserve estimation using paid and incurred claims information

Yıl 2024, Cilt: 42 Sayı: 3, 747 - 754, 12.06.2024

Müge Yeldan Yasemin Saykan

Öz

Insurance companies need to estimate accurately the possible future claims payments and thus allocate sufficient reserves to avoid financial difficulties. Reserve estimates are usually based on historical data from various sources of information. In classical reserve estimation methods, the reserve estimate is based on either paid claims information only or incurred claims information. Since all claims are eventually settled, in theory, the ultimate claim estimates obtained using paid or incurred claims data are expected to become equal. In practice, however, the ultimate estimates obtained using these two sources of information generally differ. Therefore, methods have been developed that use both sources of information to obtain the same or similar estimates. Munich Chain Ladder, Extended Complementary Loss Ratio and Paid-Incurred Chain methods are among the widely used ones. In the Turkish insurance sector, reserves are estimated using the Chain Ladder method and the Munich method. This study aims to investigate the alternative method for estimating reserves for Turkish Highways Motor Vehicles Compulsory Liability Insurance. Reserves are estimated using all these methods. Based on mean squared error, it is concluded that the Paid Incurred Chain method can be an alternative.

Anahtar Kelimeler

Claim Reserve, Extended Complementary Loss Ratio Method, Mack’s Chain Ladder Method, Munich Chain Ladder Method, Paid-Incurred Chain Method

Kaynakça

• [1] Halliwell LJ. Conjoint prediction of paid and incurred losses. Available at: https://www.casact.org/sites/default/files/database/forum_97sforum_97sf1241.pdf. Accessed on May 7, 2024.
• [2] Quarg G, Mack T. Munich chain ladder: A reserving method that reduces the gap between IBNR projections based on paid losses and IBNR projections based on incurred losses. Variance 2004;2:266–299. [CrossRef]
• [3] Halliwell LJ. Modeling paid and incurred losses together. Available at: https://citeseerx.ist.psu.edu/document? repid=rep1&type=pdf&doi=d5e4cff32cd837431b2fa64928b869783624c137. Accessed on May 7, 2024.
• [4] Dahms R. A loss reserving method for ıncomplete data. Available at: https://www.actuaries.org/ASTIN/Colloquia/Manchester/Papers/dahms_paper_final.pdf. Accessed on May 7, 2024.
• [5] Posthuma B, Cator EA, Veerkamp W, Zwet EW Van. Combined analysis of paid and ıncurred losses. Available at: https://citeseerx.ist.psu.edu/document? repid=rep1&type=pdf&doi=10d082cb72b7bfe90dce4a137c7ba87e993a46cf. Accessed on May 7, 2024.
• [6] Merz M, Wüthrich MV. Paid–incurred chain claims reserving method. Insur Math Econ 2010;46:568–579. [CrossRef]
• [7] Hertig J. A statistical approach To IBNR-reserves in marine reinsurance. ASTIN Bull 1983;15:171–183.
• [8] Gogol D. Using expected loss ratios in reserving. Insur Math Econ 1993;12:297–299. [CrossRef]
• [9] Merz M, Wüthrich M. Estimation of tail development factors in the paid-incurred chain reserving method. Casualty Actuar Soc 2013;7:61–73.
• [10] Happ S, Wüthrich MV. Paid-incurred chain reserving method with dependence modeling. ASTIN Bull 2013;43:120. [CrossRef]
• [11] Peters GW, Dong AXD, Kohn R. A copula based Bayesian approach for paid-incurred claims models for non-life insurance reserving. Insur Math Econ 2014;59:258–278. [CrossRef]
• [12] Happ S, Merz M, Wüthrich MV. Claims development result in the paid-incurred chain reserving method. Insur Math Econ 2012;51:66–72. [CrossRef]
• [13] Pigeon M, Antonio K, Denuit M. Individual loss reserving using paid-incurred data. Insur Math Econ 2014;58:121–131. [CrossRef]
• [14] Antonio K, Plat R. Micro-level stochastic loss reserving for general insurance. Scand Actuar J 2014;2014:649–669. [CrossRef]
• [15] Heberle J. Prediction of the ultimate claims based on cumulative payments and claims-incurred data using Kalman-filter theory. Ger J Insur 2015;104:39–55. [CrossRef]
• [16] Dupin G, Koenig E, Le Moine P, Monfort A, Ratiarison E. Coherent Incurred Paid (Cip) Models for claims reserving. ASTIN Bull 2018;48:749–777.
• [17] Verrall R, Nielsen JP, Jessen AH. Prediction of RBNS and IBNR claims using claim amounts and claim counts. ASTIN Bull 2010;40:871–887.
• [18] Martínez M, Nielsen JP, Verrall R. Double chain ladder. ASTIN Bull 2012;40:871–887.
• [19] Wüthrich MV, Merz M. Stochastic claims reserving manual advances in dynamic modeling. Available at: https://papers.ssrn.com/sol3/papers.cfm? abstract_id=2649057. Accessed on May 7, 2024.
• [20] Mack T. Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bull 1993;23:213225. [CrossRef]
• [21] Huijuan L, Verrall R. Bootstrap estimation of the predictive distributions of reserves using paid and ıncurred claims. Variance 2010;4:121–135.