×

Applying of the extreme value theory for determining extreme claims in the automobile insurance sector: case of a China car insurance. (English. French summary) Zbl 1485.62145


MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
60G70 Extreme value theory; extremal stochastic processes
62G32 Statistics of extreme values; tail inference
PDFBibTeX XMLCite
Full Text: arXiv Link

References:

[1] karamata (1030) Karamata, J.(1930) Sur un mode de croissance régulière des fonctions. Math-ematica (Cluj), 4, 38-53 · JFM 56.0907.01
[2] Resnick (1987) Resnick, S.I. (1987). Extreme Values, Regular Variation and Point Processes. Springer-Verbag, New-York. (MR0900810) · Zbl 0633.60001
[3] de Haan (1970) de Haan, L. (1970). On regular variation and its application to the weak conver-gence of sample extremes. Mathematical Centre Tracts, 32, Amsterdam. (MR0286156) · Zbl 0226.60039
[4] Galambos (1985) Galambos, J. (1985). The Asymptotic theory of Extreme Order Statistics. Wi-ley, New-York. (MR0489334)
[5] de Haan and Feireira (2006) de Haan, L. and Feireira A. (2006). Extreme value theory: An intro-duction. Springer. (MR2234156) · Zbl 1101.62002
[6] D. Diawara, L. Kane, S. Dembele and G.S. Lo, Afrika Statistika, Vol. 16 (3), 2021, 2883 -2909. Applying of the Extreme Value Theory for determining extreme claims in the automobile insurance sector: Case of a China car insurance 2908 · Zbl 1485.62145
[7] Rolski et al.(1999) Rolski, T., Schmidt, V., and Teugels, J.(1999). Stochastic Processes for Insur-ance and Finance. John Wiley & Sons. · Zbl 0940.60005
[8] Omey(2006) Omey, A.M., 2006. Subexponential distribution functions. Journal of Mathematical Sciences, 138(1), 5434-5449. · Zbl 1117.62054
[9] Lu and Bin Zhang(2016) Lu, D. and Bin Zhang, B., 2016. Some asymptotic results of the ruin probabilities in a two-dimensional renewal risk model with some strongly subexponential claims. Statistics & Probability Letters, 114, 20-29. · Zbl 1414.91217
[10] Goldie and Resnick (1988) Goldie, C.M. and Resnick, S., 1988. Distributions that are both subexponential and in the domain of attraction of an extreme-value distribution. Ad-vances in applied probability, 20(4), 706-718. · Zbl 0659.60028
[11] Gnedenko (1943) Gnedenko, B.(1943) Sur la distribution limite du terme maximum d’une série aléatoire, Annals of Mathematics, 1943, 44, 423-453 · Zbl 0063.01643
[12] CICR (2017) CICR.(2017)China insurance statistics report 2016. Available at http://www.circ.gov.cn/web/site0/tab5257/2017.
[13] Lozano-Perez (2012) Lozano-Perez, T.(2012). Autonomous Robot Vehicles. Springer Science & Business Media.
[14] Abraham et al.(2016) Abraham, H., Lee, C., and Brady, S.(2016). Autonomous Vehicles, Trust, and Driving Alternatives: A Survey of Consumer Preferences. AgeLab, Massachusetts In-stitute of Technology.
[15] Mao(2017) Mao S.(2017). Vehicles import market 2016 in China Consumption Daily. Beijing. Xian and Chiang-Ku (2018) Xian, X. and Chiang-Ku, F.(2018). Autonomous vehicles, risk per-ceptions and insurance demand: An individual survey in China. Elsevier.
[16] Embrechts et al. (1997) Embrechts, P., Klűppelberg, C., and Mikosch, T.(1997). Modelling Ex-tremal Events for Insurance and Finance. Berlin, Springer, 1997. · Zbl 0873.62116
[17] Coles (2001) Coles, S.G.(2001). An Introduction to Statistical Modeling of Extreme Val-ues.Springer Verlag, New York. · Zbl 0980.62043
[18] Fersi et al.(2011) Fersi, K., Boukhetala, K., and Ammou, S.B.(2011). Stratégie optimale de réduction de l’intervalle de confiance pour l’estimateur de la prime ajustée. Application en assurance automobile. Hal.
[19] Farah and Azevedo, (2017) Farah, H. and Azevedo, C.L.(2017). Safety analysis of passing ma-neuvers using extreme value theory.IATSS Research, 41, 12-21.
[20] Pisarenko and Rodkin(2010) Pisarenko, V.F. and Rodkin, M.V.(2010). Estimation of the Prob-ability of Strongest Seismic Disasters Based on the Extreme Value Theory. Izvestiya, Physics of the Solid Earth. Vol 50, pp. 311-324 (2014)
[21] Smith, (1985) Smith, R.L.(1985). Extreme value analysis of environmental time series: An ap-plication to trend detection in ground-level ozone (with discussion). Statistical Science, 4, 367-393. · Zbl 0955.62646
[22] Lo, (2017) Lo, G.S.(2017). Weak Convergence (IIA) -Functional and Random Aspects of the Univariate Extreme Value Theory, Spas Textbooks Series. Arxiv :DOI : http://dx.doi.org/10.16929/srm/2016.0009. · doi:10.16929/srm/2016.0009
[23] Lo (1986) Lô, G.S. (1986). Sur quelques estimateurs de l’Index d’une loi de Pareto : Estimateur de Hill, de S.Csörgő-Deheuvels-Mason, de de Haan-Resnick et loi limites de sommes de valeurs extrêmes pour une variable aléatoire dans le domaine d’attraction de Gumbel. Thèse de doctorat. Université Paris VI.
[24] Gumbel (1955) Gumbel, E.J. (1955) statistical estimation of the endurance limit,Tchnical report T-3A, Departement of Engineering, Columbia Univ. press.,New-York.
[25] Fisher and Tippet (1928) Fisher, R. and Tippet, L. Limiting Forms of the Frequency Distribution of the Largest or Smallest Member of a Sample Proceedings of the Cambridge Philosophical Society, 1928, 24, 180-190 · JFM 54.0560.05
[26] Lo et al. (2018) Lo G.S., K. T. A. Ngom M. and Diallo M.(2018). Weak Convergence (IIA) -Func-tional and Random Aspects of the Univariate Extreme Value Theory. Arxiv : 1810.01625
[27] D. Diawara, L. Kane, S. Dembele and G.S. Lo, Afrika Statistika, Vol. 16 (3), 2021, 2883 -2909. Applying of the Extreme Value Theory for determining extreme claims in the automobile insurance sector: Case of a China car insurance 2909 · Zbl 1485.62145
[28] Loève (1997) Loève,M.,(1997).Probability theory. Tome 1. Springer-verlag, 4th Edition.
[29] Feller (1968) Feller W.(1968) An introduction to Probability Theory and its Applications. Volume 2. Third Editions. John Wiley & Sons Inc., New-York. · Zbl 0155.23101
[30] Beirlant et al. (2004) Beirlant, J., Goegebeur, Y. Teugels, J.(2004). Statistics of Extremes Theory and Applications. Wiley. (MR2108013) · Zbl 1070.62036
[31] Ba et al. (2004) Ba A.D.,Deme E.H, Seck C.T. and Lo G.S.(2016). Consistency Bands for the Mean Excess Function and Application to Graphical Goodness-of-fit Test for Financial Data. Journal of Mathematical research, Vol. 8, (1).
[32] http://dx.doi.org/10.5539/jmr.v8n1p42, pp. 42-64 · doi:10.5539/jmr.v8n1p42
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.