×

A generalized loss ratio method dealing with uncertain volume measures. (English) Zbl 1390.91208

Summary: Unlike chain ladder, the loss ratio method requires volume measures. Typically, these volumes are assumed to be known. In practice, however, accurate volume measures are rarely available. We interpret the available volumes as estimators for the true volume measures and analyze the consequences for the loss ratio method. In particular, we calculate the mean squared error of prediction, including uncertainty of volume measures, and derive approximately optimal weights for the observed incremental loss ratios. We then introduce a generalization of the loss ratio method that is tailored to the situation of uncertain volume measures and calculate the prediction uncertainty of this generalized loss ratio method.

MSC:

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics

Software:

quantlet
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] ASTIN Working Party on Non-Life Reserving (2016) Non-life reserving practices report, http://www.actuaries.org.
[2] ClarkD.R. (2008) Reserving with incomplete exposure information. CAS E-Forum, Fall 2008.
[3] GluckS.M. (1997) Balancing development and trend in loss reserve analysis. Conference Paper, 1997 Annual Meeting of the Casualty Actuarial Society.
[4] GütschowT., HessK.T. and SchmidtK.D. (2017) Separation of small and large claims on the basis of collective models. Scandinavian Actuarial Journal, pp. 1-19. doi: 10.1080/03461238.2017.1394364 · Zbl 1416.91182 · doi:10.1080/03461238.2017.1394364
[5] HessK.T., SchmidtK.D. and ZocherM. (2006) Multivariate loss prediction in the multivariate additive model.Insurance Mathematics and Economics, 39, 185-191.10.1016/j.insmatheco.2006.02.004 · Zbl 1098.91072 · doi:10.1016/j.insmatheco.2006.02.004
[6] HärdleW.K. and HlávkaZ. (2007) Multivariate Statistics: Exercises and Solutions. New York: Springer. · Zbl 1183.62090
[7] JonesB.D. (2002) An introduction to premium trend. CAS Study Note.
[8] KaasR., GoovaertsM., DhaeneJ. and DenuitM. (2001) Modern Actuarial Risk Theory. Boston: Kluwer Academic Publishers. · Zbl 1086.91035
[9] KornU. (2016) An extension to the Cape Cod method with credibility weighted smoothing. CAS E-Forum, Summer 2016.
[10] MackTh. (2002) Schadenversicherungsmathematik. Karlsruhe: VVW.
[11] MarkowitzH. (1952) Portfolio selection. The Journal of Finance, 7(1), 77-91.
[12] MerzM. and WüthrichM. V. (2009) Prediction error of the multivariate additive loss reserving method of dependent lines of business.Variance, 3, 131-151.
[13] RiegelU. (2014) A bifurcation approach for attritional and large losses in chain ladder calculations. ASTIN Bulletin, 44(1), 127-172.10.1017/asb.2013.27 · Zbl 1290.91098 · doi:10.1017/asb.2013.27
[14] RiegelU. (2015) A quantitative study of chain ladder based pricing approaches for long-tail quota shares. ASTIN Bulletin, 45(2), 267-307.10.1017/asb.2015.2 · Zbl 1390.62219 · doi:10.1017/asb.2015.2
[15] RiegelU. (2016) Bifurcation of attritional and large losses in an additive IBNR environment. Scandinavian Actuarial Journal, 2016(7), 604-623.10.1080/03461238.2014.991423 · Zbl 1401.91187 · doi:10.1080/03461238.2014.991423
[16] SaluzA., BühlmannH., GislerA. and MoriconiF. (2014) Bornhuetter-Ferguson Reserving Method with Repricing. Available at SSRN: https://ssrn.com/abstract=2697167
[17] SaluzA., GislerA. and WüthrichM.V. (2011) Development pattern and prediction error for the stochastic Bornhuetter-Ferguson claims reserving method. ASTIN Bulletin, 41(2), 279-313. · Zbl 1242.91096
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.