Keywords and phrases: risk measure, estimation, heavy-tailed, Bias reduction, reinsurance.
Received: January 8, 2024; Accepted: April 8, 2024; Published: May 11, 2024
How to cite this article: Amary DIOP and El Hadji DEME, A bias-reduced estimation for reinsurance risk premiums of heavy-tailed loss distributions under random truncation, Far East Journal of Theoretical Statistics 68(2) (2024), 199-226. https://doi.org/10.17654/0972086324012
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License ![](/admin/tinymce_uploads/cc pic1.png) ![](/admin/tinymce_uploads/cc pic2.png)
References:
[1] C. Acerbi, Spectral measures of risk: a coherent representation of subjective risk aversion, Journal of Banking & Finance 26(7) (2002), 1505-1518. [2] C. Acerbi and D. Tasche, Expected shortfall: a natural coherent alternative to value at-risk, Economic Notes 31(2) (2002), 379-388. [3] P. Artzner, F. Delbaen, J. M. Eber and D. Heath, Coherent measures of risk, Math. Finance 9 (1999), 203-228. [4] S. Benchaira, D. Meraghni and A. Necir, On the asymptotic normality of the extreme value index for right-truncated data, Statist. Probab. Lett. 107 (2015), 378-384. [5] S. Benchaira, D. Meraghni and A. Necir, Tail product-limit process for truncated data with application to extreme value index estimation, Extremes 19 (2016a), 219-251. [6] L. J. Bruce and Ricardas Kitikis, Empirical estimation of risk measure and related quantities, North American Actuarial Journal 7(4) (2003), 44-54. [7] N. H. Bingham, C. M. Goldie and J. L. Teugels, Regular variation, Encyclopedia of Mathematics and its Applications, Cambridge University Press, Vol. 27, 1987. [8] A. Charpentier and M. Denuit, Mathématiques de l’assurance non-vie, Tome 1: Principes Fondamentaux de Théorie du Risque, Economica, 2004. [9] L. De Haan and A. Ferreira, Extreme Value Theory: An Introduction, Springer, 2006. [10] D. Denneberg, Non-additive Measure and Integral, Kluwer, Dordrecht, 1994. [11] J. Dhaene, S. Vanduffel, Q. Tang, M. J. Goovaerts, R. Kaas and D. Vyncke, Risk measures and comonotonicity: a review, Stochastic Models 22 (2006), 573-606. [12] L. Garde and G. Stupfler, Estimating extreme quantiles under random truncation, TEST 24 (2015), 207-227. [13] N. Haous, A. Necir and B. Brahim, Estimating the second-order parameter of regular variation and bias reduction in tail index estimation under random truncation, Journal of Statistical Theory and Practice 13(7) (2019), 33. [14] R. Kass, M. Goovaerts, J. Dhaene and M. Denuit, Modern Actuarial Risk Theory, Using R, Springer-Verlag, Berlin, 2008. [15] D. B. Madan and W. Schoutens, Conic financial markets and corporate finance, 2010. http://papers.ssrn.com/sol3/papers.cfm?abstractid=1547022. [16] G. Matthys, E. Delafosse, A. Guillou and J. Beirlant, Estimating catastrophic quantile levels for heavy-tailed distributions. Insurance Math. Econom. 34 (2004), 517-537. [17] H. Markowitz, Portfolio selection, Journal of Finance 7 (1952), 77-91. [18] R. D. Reiss and M. Thomas, Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields, 3rd ed., Birkhäuser Verlag, Basel, Boston, Berlin, 2007. [19] R. T. Rockafellar and S. Uryasev, Optimisation of conditional value-at-risk, The Journal of Risk 2(3) (2000), 21-41. [20] R. T. Rockafellar and S. Uryasev, Conditional value-at-risk for general loss distribution, Journal of Banking and Finance 26 (2002), 1442-1471. [21] S. Wang, Insurance pricing and increased limits ratemaking by proportional hazard transforms, Insurance Math. Econom. 17 (1995), 43-54. [22] S. Wang, Premium calculation by transforming the layer premium density, Astin Bull. 226 (1996), 71-92. [23] J. L. Wirch and M. R. Hardy, A synthesis of risk measures for capital adequacy, Insurance Math. Econom. 25 (1999), 337-347. [24] M. Woodroofe, Estimating a distribution function with truncated data, Ann. Statist. 13 (1985), 163-177. [25] M. Yaari, The dual theory of choice under risk, Econometrica 55 (1987), 95-115.
|