×

zbMATH — the first resource for mathematics

Model uncertainty in claims reserving within Tweedie’s compound Poisson models. (English) Zbl 1203.91114
Summary: We examine the claims reserving problem using Tweedie’s compound Poisson model. We develop the maximum likelihood and Bayesian Markov chain Monte Carlo simulation approaches to fit the model and then compare the estimated models under different scenarios. The key point we demonstrate relates to the comparison of reserving quantities with and without model uncertainty incorporated into the prediction. We consider both the model selection problem and the model averaging solutions for the predicted reserves. As a part of this process we also consider the sub problem of variable selection to obtain a parsimonious representation of the model being fitted.

MSC:
91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Proceedings of London Mathematical Society 38 pp 257– (1935)
[2] Stochastic Claims Reserving Methods in Insurance (2008) · Zbl 1273.91011
[3] DOI: 10.1017/S1357321700003809
[4] DOI: 10.1007/s11222-005-4070-y
[5] DOI: 10.1016/j.csda.2004.08.001 · Zbl 1330.62115
[6] The American Statistician 46 pp 167– (1992)
[7] Journal of the Royal Statististical Society 57 pp 473– (1995)
[8] Insurance: Mathematics and Economics 27 pp 313– (2000)
[9] DOI: 10.1017/S0515036100013490
[10] Bayesian Theory (1994) · Zbl 0796.62002
[11] DOI: 10.1002/cjs.5550360401 · Zbl 1167.60344
[12] DOI: 10.3150/bj/1130077595 · Zbl 1085.62097
[13] DOI: 10.2143/AST.32.1.1020 · Zbl 1094.91514
[14] Journal of Royal Statistical Society 55 pp 3– (1993)
[15] DOI: 10.1016/j.csda.2007.02.021 · Zbl 1203.62001
[16] DOI: 10.1214/ss/1015346320 · Zbl 1127.65305
[17] Monte Carlo Statistical Methods (2004) · Zbl 1096.62003
[18] Scandinavian Actuarial Journal pp 69– (1994)
[19] DOI: 10.1093/biomet/82.4.711 · Zbl 0861.62023
[20] Markov Chain Monte Carlo in Practice (1996) · Zbl 0832.00018
[21] DOI: 10.1214/aoap/1034625254 · Zbl 0876.60015
[22] Bayesian Data Analysis (1995)
[23] Proceeding of the Indian Statistical Institute Golden Jubilee International Conference pp 579– (1984)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.