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Volumn 45, Issue 1, 2009, Pages 49-58

Empirical estimation of the proportional hazard premium for heavy-tailed claim amounts

Author keywords

Extreme values; Heavy tails; Hill estimator; L statistics; Risk premium

Indexed keywords


EID: 67650071002     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.insmatheco.2009.03.004     Document Type: Article
Times cited : (24)

References (44)
  • 1
    • 0011521721 scopus 로고
    • Asymptotic normality of Hill's estimator
    • Extreme Value Theory (Oberwolfach, 1987), Springer, New York
    • Beirlant J., and Teugels J. Asymptotic normality of Hill's estimator. Extreme Value Theory (Oberwolfach, 1987). Lecture Notes in Statistics vol. 51 (1989), Springer, New York 148-155
    • (1989) Lecture Notes in Statistics , vol.51 , pp. 148-155
    • Beirlant, J.1    Teugels, J.2
  • 4
    • 84893363642 scopus 로고    scopus 로고
    • Applying the proportional hazard premium calculation principle
    • Centeno M.L., and Andrade e Silva J. Applying the proportional hazard premium calculation principle. Astin Bulletin 35 (2005) 409-425
    • (2005) Astin Bulletin , vol.35 , pp. 409-425
    • Centeno, M.L.1    Andrade e Silva, J.2
  • 5
    • 33645029334 scopus 로고    scopus 로고
    • Confidence intervals for the tail index
    • Cheng S., and Peng L. Confidence intervals for the tail index. Bernoulli 7 (2001) 751-760
    • (2001) Bernoulli , vol.7 , pp. 751-760
    • Cheng, S.1    Peng, L.2
  • 6
    • 0002530923 scopus 로고
    • Asymptotic distribution of linear combinations of functions of order statistics with applications to estimation
    • Chernoff H., Gastwirth J.L., and Johns M.V. Asymptotic distribution of linear combinations of functions of order statistics with applications to estimation. Annals of Mathematical Statistics 38 (1967) 52-72
    • (1967) Annals of Mathematical Statistics , vol.38 , pp. 52-72
    • Chernoff, H.1    Gastwirth, J.L.2    Johns, M.V.3
  • 13
    • 0001591373 scopus 로고
    • On the estimation of the extreme-value index and large quantile estimation
    • Dekkers A.L.M., and de Haan L. On the estimation of the extreme-value index and large quantile estimation. Annals of Statistics 17 (1989) 1795-1832
    • (1989) Annals of Statistics , vol.17 , pp. 1795-1832
    • Dekkers, A.L.M.1    de Haan, L.2
  • 14
    • 0001760675 scopus 로고
    • A moment estimator for the index of an extreme-value distribution
    • Dekkers A.L.M., Einmahl J.H.J., and de Haan L. A moment estimator for the index of an extreme-value distribution. Annals of Statistics 17 (1989) 1833-1855
    • (1989) Annals of Statistics , vol.17 , pp. 1833-1855
    • Dekkers, A.L.M.1    Einmahl, J.H.J.2    de Haan, L.3
  • 15
    • 0001080355 scopus 로고
    • Optimal choice of sample fraction in extreme-value estimation
    • Dekkers A.L.M., and de Haan L. Optimal choice of sample fraction in extreme-value estimation. Journal of Multivariate Analysis 47 (1993) 173-195
    • (1993) Journal of Multivariate Analysis , vol.47 , pp. 173-195
    • Dekkers, A.L.M.1    de Haan, L.2
  • 16
    • 0001061726 scopus 로고    scopus 로고
    • Selection of the optimal sample fraction in univariate extreme value estimation
    • Drees H., and Kaufmann E. Selection of the optimal sample fraction in univariate extreme value estimation. Stochastic Processes and Applications 75 (1998) 149-195
    • (1998) Stochastic Processes and Applications , vol.75 , pp. 149-195
    • Drees, H.1    Kaufmann, E.2
  • 18
    • 21644487570 scopus 로고    scopus 로고
    • Asymptotically best linear unbiased tail estimators under a second-order regular variation condition
    • Gomes M.I., Figueiredo F., and Mendonça S. Asymptotically best linear unbiased tail estimators under a second-order regular variation condition. Journal of Statistical Planning and Inference 134 (2005) 409-433
    • (2005) Journal of Statistical Planning and Inference , vol.134 , pp. 409-433
    • Gomes, M.I.1    Figueiredo, F.2    Mendonça, S.3
  • 19
    • 0005358897 scopus 로고
    • Edgeworth expansions for linear combinations of order statistics
    • Amsterdam Mathematisch Centrum
    • Helmers R. Edgeworth expansions for linear combinations of order statistics. Mathematical Center Tracts vol. 105 (1982), Amsterdam Mathematisch Centrum
    • (1982) Mathematical Center Tracts , vol.105
    • Helmers, R.1
  • 20
    • 0001263124 scopus 로고
    • A simple approach to inference about the tail of a distribution
    • Hill B.M. A simple approach to inference about the tail of a distribution. Annals of Statistics 3 (1975) 1136-1174
    • (1975) Annals of Statistics , vol.3 , pp. 1136-1174
    • Hill, B.M.1
  • 22
    • 67650071479 scopus 로고    scopus 로고
    • Estimating the mean of heavy-tailed distributions
    • Johansson J. Estimating the mean of heavy-tailed distributions. Extremes 6 (2003) 91-109
    • (2003) Extremes , vol.6 , pp. 91-109
    • Johansson, J.1
  • 23
    • 85011163899 scopus 로고    scopus 로고
    • Empirical estimation of risk measures and related quantities
    • Jones B.L., and Zitikis R. Empirical estimation of risk measures and related quantities. North American Actuarial Journal 7 (2003) 44-54
    • (2003) North American Actuarial Journal , vol.7 , pp. 44-54
    • Jones, B.L.1    Zitikis, R.2
  • 24
    • 33644869389 scopus 로고    scopus 로고
    • Testing for the order of risk measures: An application of L-statistics in actuarial science
    • Jones B.L., and Zitikis R. Testing for the order of risk measures: An application of L-statistics in actuarial science. Metron 63 (2005) 193-211
    • (2005) Metron , vol.63 , pp. 193-211
    • Jones, B.L.1    Zitikis, R.2
  • 25
    • 34447101114 scopus 로고    scopus 로고
    • Risk measures, distortion parameters, and their empirical estimation
    • Jones B.L., and Zitikis R. Risk measures, distortion parameters, and their empirical estimation. Insurance: Mathematics and Economics 41 (2007) 279-297
    • (2007) Insurance: Mathematics and Economics , vol.41 , pp. 279-297
    • Jones, B.L.1    Zitikis, R.2
  • 26
    • 0346665594 scopus 로고
    • Asymptotic normality of linear combinations of order statistics with a smooth score function
    • Mason D.M. Asymptotic normality of linear combinations of order statistics with a smooth score function. Annals of Statistics 9 (1981) 899-908
    • (1981) Annals of Statistics , vol.9 , pp. 899-908
    • Mason, D.M.1
  • 27
    • 0000782528 scopus 로고
    • Laws of the large numbers for sums of extreme values
    • Mason D.M. Laws of the large numbers for sums of extreme values. Annals of Probability 10 (1982) 754-764
    • (1982) Annals of Probability , vol.10 , pp. 754-764
    • Mason, D.M.1
  • 28
    • 0141573196 scopus 로고    scopus 로고
    • Estimating the extreme value index and high quantiles with exponential regression models
    • Matthys G., and Beirlant J. Estimating the extreme value index and high quantiles with exponential regression models. Statistica Sinica 13 (2003) 853-880
    • (2003) Statistica Sinica , vol.13 , pp. 853-880
    • Matthys, G.1    Beirlant, J.2
  • 29
    • 67650068365 scopus 로고    scopus 로고
    • Estimating the risk adjusted premium of the largest reinsurance covers
    • Antoch J. (Ed), Physica-Verlag, Springer. 3-7908-1554-3
    • Necir A., and Boukhetala K. Estimating the risk adjusted premium of the largest reinsurance covers. In: Antoch J. (Ed). Proceeding of Computational Statistics (2004), Physica-Verlag, Springer. 3-7908-1554-3 1577-1584
    • (2004) Proceeding of Computational Statistics , pp. 1577-1584
    • Necir, A.1    Boukhetala, K.2
  • 30
    • 28044440075 scopus 로고    scopus 로고
    • A functional law of the iterated logarithm for kernel type estimators of the tail index
    • Necir A. A functional law of the iterated logarithm for kernel type estimators of the tail index. Journal of Statistical Planning and Inference 136 (2006) 780-802
    • (2006) Journal of Statistical Planning and Inference , vol.136 , pp. 780-802
    • Necir, A.1
  • 31
    • 67650020188 scopus 로고    scopus 로고
    • Statistical estimate of the proportional hazard premium of loss
    • Necir A., Meraghni D., and Meddi F. Statistical estimate of the proportional hazard premium of loss. Scandinavian Actuarial Journal 3 (2007) 147-161
    • (2007) Scandinavian Actuarial Journal , vol.3 , pp. 147-161
    • Necir, A.1    Meraghni, D.2    Meddi, F.3
  • 33
    • 0041364621 scopus 로고    scopus 로고
    • Estimating the mean of a heavy-tailed distribution
    • Peng L. Estimating the mean of a heavy-tailed distribution. Statistic and Probability Letters 52 (2001) 255-264
    • (2001) Statistic and Probability Letters , vol.52 , pp. 255-264
    • Peng, L.1
  • 36
    • 0011624543 scopus 로고
    • Asymptotic normality of linear combinations of function of order statistics
    • Shorack G.R. Asymptotic normality of linear combinations of function of order statistics. Annals of Mathematical Statistics 40 (1969) 2041-2050
    • (1969) Annals of Mathematical Statistics , vol.40 , pp. 2041-2050
    • Shorack, G.R.1
  • 38
    • 0001523476 scopus 로고
    • Linear functions of order statistics with smooth weight functions
    • Stigler S. Linear functions of order statistics with smooth weight functions. Annals of Statistics 2 (1974) 676-693
    • (1974) Annals of Statistics , vol.2 , pp. 676-693
    • Stigler, S.1
  • 39
    • 33646495325 scopus 로고    scopus 로고
    • On univariate extreme value statistics and the estimation of reinsurance premiums
    • Vandewalle B., and Beirlant J. On univariate extreme value statistics and the estimation of reinsurance premiums. Insurance: Mathematics and Economics 38 (2006) 441-459
    • (2006) Insurance: Mathematics and Economics , vol.38 , pp. 441-459
    • Vandewalle, B.1    Beirlant, J.2
  • 40
    • 85011528623 scopus 로고    scopus 로고
    • Premium calculation by transforming the layer premium density
    • Wang S.S. Premium calculation by transforming the layer premium density. ASTIN Bulletin 26 (1996) 71-92
    • (1996) ASTIN Bulletin , vol.26 , pp. 71-92
    • Wang, S.S.1
  • 41
    • 84936167519 scopus 로고
    • Estimation of parameters and large quantiles based on the k largest observations
    • Weissman I. Estimation of parameters and large quantiles based on the k largest observations. Journal of American Statistical Association 73 (1978) 812-815
    • (1978) Journal of American Statistical Association , vol.73 , pp. 812-815
    • Weissman, I.1
  • 42
    • 0002812608 scopus 로고
    • Limit theorems for the ratio of the empirical distribution function to the true distribution function
    • Wellner J.A. Limit theorems for the ratio of the empirical distribution function to the true distribution function. Zeitschrift für Wahrscheinlichkeitstheorie und verwande Gebiete 45 (1978) 73-88
    • (1978) Zeitschrift für Wahrscheinlichkeitstheorie und verwande Gebiete , vol.45 , pp. 73-88
    • Wellner, J.A.1
  • 43
    • 0002569928 scopus 로고
    • The dual theory of choice under risk
    • Yaari M.E. The dual theory of choice under risk. Econometrica 55 (1987) 95-115
    • (1987) Econometrica , vol.55 , pp. 95-115
    • Yaari, M.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.