Bayesian modelling of outstanding liabilities incorporating claim count uncertainty. (English) Zbl 1084.62544
Summary: This paper deals with the prediction of the amount of outstanding automobile claims that an insurance company will pay in the near future. We consider various competing models using Bayesian theory and Markov chain Monte Carlo methods. Claim counts are used in order to add a further hierarchical stage in the model with log-normally distributed claim amounts and its corresponding state space version. By this way, we incorporate information from both the outstanding claim amounts and counts data resulting to new model formulations. We provide implementation details and illustrations with real insurance data.
MSC:
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 62F15 | Bayesian inference |
| 65C40 | Numerical analysis or methods applied to Markov chains |
References:
| [1] | Agresti A., Categorical Data Analysis (1990) · Zbl 0716.62001 |
| [2] | De Alba E., Transactions of the International Congress of Actuaries (1998) |
| [3] | Besag J., Journal of the Royal Statistical Society B 55 pp 25– (1993) |
| [4] | Brooks S.P., Statistics and Computing 8 pp 319– (1999) · doi:10.1023/A:1008820505350 |
| [5] | Carlin B.P., Insurance: Mathematics and Economics 11 pp 209– (1992) · Zbl 0764.62087 · doi:10.1016/0167-6687(92)90027-9 |
| [6] | Carlin B.P., Journal of the American Statistical Association 87 pp 493– (1992) · doi:10.1080/01621459.1992.10475231 |
| [7] | Carter C.K., Biometrika 81 pp 541– (1994) · Zbl 0809.62087 · doi:10.1093/biomet/81.3.541 |
| [8] | Cowles M.K., Journal of the American Statistical Association 91 pp 883– (1996) · doi:10.1080/01621459.1996.10476956 |
| [9] | De Jong P., The Journal of the Institute of Actuaries 110 pp 157– (1983) · doi:10.1017/S0020268100041287 |
| [10] | Dellaportas P., Applied Statistics 42 pp 443– (1993) · Zbl 0825.62409 · doi:10.2307/2986324 |
| [11] | Gamerman D., Biometrika 85 pp 215– (1998) · Zbl 0904.62083 · doi:10.1093/biomet/85.1.215 |
| [12] | Gelfand A.E., Bayesian Statistics pp 147– (1992) |
| [13] | Gelfand A.E., Biometrika 85 pp 1– (1998) · Zbl 0904.62036 · doi:10.1093/biomet/85.1.1 |
| [14] | Gelfand A.E., Journal of the American Statistical Association 85 pp 972– (1990) · doi:10.1080/01621459.1990.10474968 |
| [15] | Gelfand A.E., Journal of the American Statistical Association 87 pp 523– (1992) · doi:10.1080/01621459.1992.10475235 |
| [16] | Geweke J., Bayesian Statistics pp 169– (1992) · Zbl 1093.62107 |
| [17] | Gilks W.R., Markov Chain Monte Carlo in Practice (1996) · Zbl 0832.00018 |
| [18] | Gilks W.R., Applied Statistics 41 pp 337– (1992) · Zbl 0825.62407 · doi:10.2307/2347565 |
| [19] | Haastrup S., Astin Bulletin 26 pp 139– (1996) · doi:10.2143/AST.26.2.563216 |
| [20] | Haberman S., The Statistician 45 pp 407– (1996) · doi:10.2307/2988543 |
| [21] | Heidelberger P., Operations Research 31 pp 1109– (1983) · Zbl 0532.65097 · doi:10.1287/opre.31.6.1109 |
| [22] | Hesselager O., Scandinavian Actuarial Journal 1991 pp 25– (1991) · Zbl 0778.62097 · doi:10.1080/03461238.1991.10557358 |
| [23] | Jewell W.S, Astin Bulletin 19 pp 25– (1989) · doi:10.2143/AST.19.1.2014914 |
| [24] | Kass R.E., Journal of American Statistical Association 91 pp 1343– (1996) · doi:10.1080/01621459.1996.10477003 |
| [25] | Laud P.W., Journal of the Royal Statistical Society B 57 pp 247– (1995) |
| [26] | Makov U.E., The Statistician 45 pp 503– (1996) · doi:10.2307/2988548 |
| [27] | Neuhaus W., Scandinavian Actuarial Journal 1992 pp 97– (1992) · Zbl 0770.62093 · doi:10.1080/03461238.1992.10413901 |
| [28] | Norberg R., Scandinavian Actuarial Journal 1986 pp 155– (1986) · Zbl 0648.62106 · doi:10.1080/03461238.1986.10413806 |
| [29] | Raftery A.L., Bayesian Statistics 4 pp 763– (1992) |
| [30] | Renshaw A.E., The Journal of the Institute of Actuaries 116 pp 559– (1989) · doi:10.1017/S0020268100036702 |
| [31] | Renshaw A., Actuarial Research Paper 65 (1994) |
| [32] | Renshaw A., British Actuarial Journal 4 pp 903– (1998) · doi:10.1017/S1357321700000222 |
| [33] | Rosenberg M.A., North American Actuarial Journal 3 (2) pp 130– (1999) · Zbl 1082.62503 · doi:10.1080/10920277.1999.10595808 |
| [34] | Scollnik D.P.M., Astin Bulletin 28 (1) pp 135– (1998) · Zbl 1168.60311 · doi:10.2143/AST.28.1.519083 |
| [35] | Scollnik D.P.M., North American Actuarial Journal 5 (2) pp 96– (2001) · Zbl 1083.62543 · doi:10.1080/10920277.2001.10595987 |
| [36] | Smith A.F.M., Journal of the Royal Statistical Society B 55 pp 3– (1993) |
| [37] | Taylor G.C., Journal of Econometrics 23 pp 37– (1983) · doi:10.1016/0304-4076(83)90074-X |
| [38] | Verrall R, The Journal of the Institute of Actuaries 116 pp 589– (1989) · doi:10.1017/S0020268100036714 |
| [39] | Verrall R., Astin Bulletin 20 pp 217– (1990) · doi:10.2143/AST.20.2.2005444 |
| [40] | Verrall R., The Journal of the Institute of Actuaries 118 pp 489– (1991) · doi:10.1017/S0020268100019545 |
| [41] | Verrall R, The Journal of the Institute of Actuaries 120 pp 171– (1993) · doi:10.1017/S0020268100036891 |
| [42] | Verrall R., Astin Bulletin 24 pp 325– (1994) · doi:10.2143/AST.24.2.2005074 |
| [43] | Verrall R., Insurance: Mathematics and Economics 19 pp 31– (1996) · Zbl 0894.62114 · doi:10.1016/S0167-6687(96)00000-5 |
| [44] | Verrall R., Insurance: Mathematics and Economics 26 pp 91– (2000) · Zbl 1072.62654 · doi:10.1016/S0167-6687(99)00038-4 |
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.
