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Abstract
The claim reserve is the amount of funds the insurance company must set aside to pay claims reported by policyholders. Estimation of claim reserves is carried out as a preventive step for failed payment if the reported claim exceeds the insurance company’s capacity. The estimation of claim reserves in this study was performed using the double chain ladder method with a bootstrap approach. The data used was in the form of a run-off triangle of claim counts and claim amounts presented in incremental and cumulative form. The purpose of this research was to determine the estimated value of reported but not settled (RBNS) and incurred but not reported (IBNR) claim reserves through the bootstrap application on the double chain ladder method. After performing the double chain ladder calculation, the estimated RBNS claim reserves amounted to 6,828,456,000 and the IBNR amounted to 3,714,144,000. Meanwhile, using the bootstrap approach, the RBNS claim reserve estimate was 6,777,539,000 and the IBNR was 3,741,979,000. With the conclusion that the greater the nominal claim reserve allocated, the lower the chance of the company going bankrupt.
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References
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References
H.H. Panjer and G.E. Willmot, Insurance Risk Models. Schaumburg, IL, USA: Society of Actuaries, 1992.
M.J. Khalifatullah, K. Anggaraputra, T.D. Dumamika, A.Z. Soleh, and L. Noviyanti, “Comparison of estimated reserve claims with the classical chain ladder and bornhuetter-double chain ladder method,” J. Mat. Stat. Komput., vol. 20, no. 1, pp. 207–220, Sep. 2023, doi: 10.20956/j.v20i1.27673.
S.A. Pertiwi, I.N. Widana, and K. Sari, “Estimasi cadangan klaim pada asuransi umum dengan metode chain ladder,” E-J. Mat., vol. 12, no. 1, pp. 71–76, Jan. 2023, doi: 10.24843/MTK.2023.v12.i01.p402.
A.A. Soleha and Y. Hikmah, “Claim reserve estimation using double chain ladder method,” Int. J. Ind. Eng. Prod. Res., vol. 33, no. 4, pp. 1–8, 2022, doi: 10.22068/ijiepr.33.4.2.
N.L. Bowers, H.U. Gerber, J.C. Hickman, D.A. Jones, and C.J. Nesbitt, Actuarial Mathematics. Schaumburg, IL, USA: Society of Actuaries, 1998.
S.M. Maher, S.J. Rulis, and S P. Melek, “Claim reserves,” in Valuat. Actuary Symp., 1992, pp. 1–40.
F.F. Adam, “Claim reserving estimation by using the chain ladder method," KnE Soc. Sci., vol. 3, no. 11, Aug. 2018, pp. 1192–1204, doi: 10.18502/kss.v3i11.2840.
T. Agbeko, M. Hiabu, M.D.M. Miranda, J.P. Nielsen, and R. Verrall, “Validating the double chain ladder stochastic claims reserving model,” Var. Adv. Sci. Risk, vol. 8, no. 2, pp. 138–160, 2014.
M.D.M. Miranda, J.P. Nielsen, R. Verral, and M.V. Wuthrich, “Double chain ladder, claims development inflation and zero claims,” Scand. Actuar. J., vol. 2015, no. 2, pp. 383–405, 2015, doi: 10.1080/03461238.2013.823459.
L. Schoepf, “On the double chain ladder for reserve estimation with bootstrap applications,” Master thesis, Missouri University of Science and Technology, Rolla, MO, USA, 2016.
A.K. Mutaqin, D.R. Tampubolon, and S. Darwis, “Run-off triangle data dan permasalahannya,” Statistika, vol. 8, no. 1, pp. 55–59, 2008, doi: 10.29313/jstat.v8i1.975.
T. Mack, “Distribution-free calculation of the standard error of chain ladder reserve estimates,” Astin Bull., J. IAA, vol. 23, no. 2, pp. 213–225, Nov. 1993, doi: 10.2143/AST.23.2.2005092.
R. Verrall, J.P. Nielsen, and A.H. Jessen, “Prediction of RBNS and IBNR claims using claim amounts and claim counts,” Astin Bull., J. IAA, vol. 40, no. 2, pp. 871–887, Nov. 2010, doi: 10.2143/AST.40.2.2061139.
M.D.M. Miranda, J.P. Nielsen, and R. Verrall, “Double chain ladder,” Astin Bull., J. IAA, vol. 42, no. 1, pp. 59–76, May 2012, doi: 10.2143/AST.42.1.216071.
M.D.M. Miranda, B. Nielsen, J.P. Nielsen, and R. Verrall, “Cash flow simulation for a model of outstanding liabilities based on claim amounts,” Astin Bull., J. IAA, vol. 41, no. 1, pp. 107-129, May 2011, doi: 10.2143/AST.41.1.2084388.