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On impact of largest claims reinsurance treaties on the ceding company’s loss reserve

Part of: Applications Stochastic processes Decision theory

Published online by Cambridge University Press:  01 February 2023

Fatemeh Atatalab  and
Amir T Payandeh Najafabadi Open the ORCID record for Amir T Payandeh Najafabadi [Opens in a new window]
Fatemeh Atatalab
Affiliation:
Department of Actuarial Science, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, 1983969411 Tehran, Iran
Amir T Payandeh Najafabadi*
Affiliation:
Department of Actuarial Science, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, 1983969411 Tehran, Iran
*
*Corresponding author. E-mail: [email protected]
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Abstract

This article examines the impact of the largest claims reinsurance treaties on loss reserve of the ceding company. The largest claims reinsurance, known as LCR, and ECOMOR reinsurance treaties are considered to be the two most appropriate reinsurance treaties for large or catastrophe claims. Then, it studies the impact of such treaties on loss reserves. Through a simulation study, it shown that, under a more general situation, the LCR treaty can be a more efficient (in some sense, see below) treaty than the ECOMOR treaty for the ceding company.

Keywords

Loss reserveReinsuranceMean square error of predictionSimulation

MSC classification

Primary: 62P05: Applications to actuarial sciences and financial mathematics
Secondary: 60G25: Prediction theory 62C05: General considerations
Type
Original Research Paper
Information
Annals of Actuarial Science , Volume 17 , Issue 2 , July 2023 , pp. 328 - 357
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Institute and Faculty of Actuaries

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References

Albrecher, H., Beirlant, J. & Teugels, J.L. (2017). Reinsurance: Actuarial and Statistical Aspects. John Wiley & Sons.CrossRefGoogle Scholar
Berglund, R.M. (1998). A note on the net premium for a generalized largest claims reinsurance cover. ASTIN Bulletin, 28(1), 153–162.CrossRefGoogle Scholar
Buchwalder, M., Bühlmann, H., Merz, M. & Wüthrich, M.V. (2006). The mean square error of prediction in the chain ladder reserving method (Mack and Murphy revisited). ASTIN Bulletin, 36, 521–542.CrossRefGoogle Scholar
Bühlmann, H., Straub, E. & Schnieper, R. (1980). Claims reserves in casualty insurance based on a probabilistic model. Mitteilungen der Vereinidung Schweizerischer Versicherungsmathematiker, 1, 21–46.Google Scholar
Craighead, D.H. (1994). Reserving for catastrophe reinsurance. Journal of the Institute of Actuaries, 121(1), 135–160.CrossRefGoogle Scholar
David, H.A. & Nagaraja, H.N. (2003). Order Statistics, 3rd edition. Wiley.Google Scholar
England, P.D., Verrall, R.J. & Wüthrich, M.V. (2019). On the lifetime and one-year views of reserve risk, with application to IFRS 17 and solvency II risk margins. Insurance: Mathematics and Economics, 85, 74–88.Google Scholar
Fan, Y., Griffin, P.S., Szimayer, A. & Wang, T. (2017). The effect of largest claim and excess of loss reinsurance on a company’s ruin time and valuation. Risks, 5(1).CrossRefGoogle Scholar
Gisler, A. & Wüthrich, M. (2008). Credibility for the chain ladder reserving method. ASTIN Bulletin, 38, 565–597.CrossRefGoogle Scholar
Hertig, J. (1985). A statistical approach to IBNR-reserves in marine reinsurance. ASTIN Bulletin: The Journal of the IAA, 15(2), 171–183.CrossRefGoogle Scholar
Hess, C. (2009). Computing the mean and the variance of the cedent’s share for largest claims reinsurance covers. Insurance: Mathematics and Economics, 44(3), 497–504 Google Scholar
Hindley, D. (2017). Claims Reserving in General Insurance. Cambridge University Press.CrossRefGoogle Scholar
Jiang, J. & Tang, Q. (2008). Reinsurance under the LCR and ECOMOR treaties with emphasis on light tailed claims. Insurance: Mathematics and Economics, 43(3), 431–436.Google Scholar
Kremer, E. (1982). Rating of largest claims and ECOMOR reinsurance treaties for large portfolios. ASTIN Bulletin, 13(1), 47–56.CrossRefGoogle Scholar
Ladoucette, S.A. & Teugels, J.L. (2006). Reinsurance of large claims. Computational and Applied Mathematics, 186(1), 163–190.CrossRefGoogle Scholar
Mack, T. (1993). Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin, 23, 214–225.CrossRefGoogle Scholar
Margraf, C., Elpidorou, V. & Wüthrich, M.V. (2018). Claim reserving in the presence of excess-of-loss reinsurance micro models based on aggregate data. Insurance: Mathematics and Economics, 80, 54–65.Google Scholar
Martinez-Miranda, M.D., Nielsen, J.P. & Verrall, R.J. (2012). Double chain ladder. ASTIN Bulletin, 42, 59–76.Google Scholar
Martinez-Miranda, M.D., Nielsen, J.P., Verrall, R.J. & Wüthrich, M.V. (2015). Double chain ladder, claims development inflation and zero-claims. Scandinavian Actuarial Journal, 383–405.CrossRefGoogle Scholar
Murphy, K. & McLennan, A. (2006). A method for projecting individual large claims. In Casualty Actuarial Society Forum (vol. 59, pp. 205–236).Google Scholar
Narayan, P. & Warthen, T. (2000). A comparative study of the performance of loss reserving methods through simulation. Journal of Actuarial Practice, 8, 63–88.Google Scholar
Panning, W.H. (2006). Measuring loss reserve uncertainties. In Casualty Actuarial Society Forum Fall 2006 (pp. 237–267).Google Scholar
Payandeh Najafabadi, A.T. & Panahi Bazaz, A. (2018). An optimal multi-layer reinsurance policy under conditional tail expectation. Annals of Actuarial Science, 12, 130–146.CrossRefGoogle Scholar
Peters, G.W., Dong, A.X. & Kohn, R. (2014). A copula based Bayesian approach for paid-incurred claims models for non-life insurance reserving. Insurance: Mathematics and Economics, 59, 258–278.Google Scholar
Riegel, U. (2015). A quantitative study of chain ladder based pricing approachs for long-tail quota shares. ASTIN Bulletin, 45(2), 267–307.CrossRefGoogle Scholar
Seal, H.L. (1969). Stochastic Theory of a Risk Business. Wiley and Sons, New York.Google Scholar
Schiegl, M. (2002). On the safety loading for chain ladder estimates: a Monte Carlo simulation study. ASTIN Bulletin: The Journal of the IAA, 32(1), 107–128.CrossRefGoogle Scholar
Stanard, J. (1985). A simulation test of prediction errors of loss reserve techniques. Proceedings of the Casualty Actuarial Society, 124–148.Google Scholar
Stelljes, S. (2006). A nonlinear regression model for incurred but not reported losses. In Casualty Actuarial Society Forum Fall 2006 (pp. 353–377).Google Scholar
Taylor, G.C. (1982). Estimation of outstanding reinsurance recoveries on the basis of incomplete information. Insurance: Mathematics and Economics, 1(1), 3–11.Google Scholar
Thepaut, A. (1950). Une nouvelle forme de reassurance. le traite d’excedent du cout moyen relatif (ECOMOR). Bulletin Trimestriel de l’Institut des Actuaires Francais, 49, 273–343.Google Scholar
Úbeda Inés, P. (2020). Modelling a Pricing Strategy for ADC Finite Risk Reinsurance Treaties with GLMM Approach . Master thesis of actuarial and financial sciences, Universitat de Barcelona.Google Scholar
Vaughan, R.L. (1998). Some extensions of J. N. Stanard’s simulation model for loss reserving. In Casualty Actuarial Society Forum Fall 1998, 415–498.Google Scholar
Veprauskaite, E. & Adams, M. (2017). Leverage and reinsurance effects on loss reserves in the United Kingdom’s property-casualty insurance industry. Accounting and Business Research, 48(4), 373–399.CrossRefGoogle Scholar
Verrall, R.J. (1991). Chain ladder and maximum likelihood. Journal of the Institute of Actuaries, 118(3), 489–499.CrossRefGoogle Scholar
Verrall, R.J., Nielsen, J.P. & Jessen, A.H. (2010). Prediction of RBNS and IBNR claims using claim amounts and claim counts. ASTIN Bulletin, 40, 871–887.Google Scholar
Winkler, M. & Kansal, S. (2020). Actuarial Challenges and IFRS 17. Available at SSRN 3670808.Google Scholar