Risk aggregation and capital allocation using a new generalized Archimedean copula

Insurance: Mathematics and Economics - Tập 102 - Trang 75-90 - 2022
Fouad Marri1, Khouzeima Moutanabbir2
1Department of Statistics and Actuarial Science, Institut National de Statistique et d'Economie Appliquée, INSEA, Morocco
2Department of Finance and Investment Management, School of Management, University of Johannesburg, Johannesburg, South Africa

Tài liệu tham khảo

Albrecher Albrecher, 2011, Explicit ruin formulas for models with dependence among risks, Insurance. Mathematics & Economics, 48, 265, 10.1016/j.insmatheco.2010.11.007 Arnold, 1983 Arnold, 2015, Pareto Distributions Basu, 1998, Order Statistics in Exponential Distribution, vol. 17, 3 Cai, 2005, Conditional tail expectations for multivariate phase-type distributions, Journal of Applied Probability, 42, 810, 10.1239/jap/1127322029 Chiragiev, 2007, Multivariate Pareto portfolios: TCE-based capital allocation and divided differences, Scandinavian Actuarial Journal, 2007, 261, 10.1080/03461230701554007 Cossette, 2013, Multivariate distribution defined with Farlie–Gumbel–Morgenstern copula and mixed Erlang marginals: aggregation and capital allocation, Insurance. Mathematics & Economics, 52, 560, 10.1016/j.insmatheco.2013.03.006 Côté, 2019, Dependence in a background risk model, Journal of Multivariate Analysis, 172, 28, 10.1016/j.jmva.2018.11.012 Cottin, 2014, From Bernstein polynomials to Bernstein copulas, Journal of Applied Functional Analysis, 9, 277 David, 2004, Order Statistics, 10.1002/0471667196.ess6023 Dhaene, 2008, Can a coherent risk measure be too subadditive?, The Journal of Risk and Insurance, 75, 365, 10.1111/j.1539-6975.2008.00264.x Diers, 2012, Dependence modeling in non-life insurance using the Bernstein copula, Insurance. Mathematics & Economics, 50, 430, 10.1016/j.insmatheco.2012.02.007 Faa di Bruno, 1855, Sullo sviluppo delle funzioni, Annali Di Scienze Matematiche E Fisiche, 6, 479 Feller, 1971 Furman, 2021, Multiplicative background risk models: setting a course for the idiosyncratic risk factors distributed phase-type, Insurance. Mathematics & Economics, 96, 153, 10.1016/j.insmatheco.2020.11.007 Furman, 2005, Risk capital decomposition for a multivariate dependent gamma portfolio, Insurance. Mathematics & Economics, 37, 635, 10.1016/j.insmatheco.2005.06.006 Furman, 2006, Tail variance premium with applications for elliptical portfolio of risks, ASTIN Bulletin, 36, 433, 10.1017/S0515036100014586 Furman, 2010, Multivariate Tweedie distributions and some related capital-at-risk analyses, Insurance. Mathematics & Economics, 46, 351, 10.1016/j.insmatheco.2009.12.001 Furman, 2008, Weighted risk capital allocations, Insurance. Mathematics & Economics, 43, 263, 10.1016/j.insmatheco.2008.07.003 Hartman, 2014, vol. 15 Hurd, 2007 Kim, 2007 Kulpa, 1999, On approximation of copulas, International Journal of Mathematics and Mathematical Sciences, 22, 259, 10.1155/S0161171299222594 Landsman, 2003, Tail conditional expectations for elliptical distributions, North American Actuarial Journal, 7, 55, 10.1080/10920277.2003.10596118 Liebscher, 2008, Construction of asymmetric multivariate copulas, Journal of Multivariate Analysis, 99, 2234, 10.1016/j.jmva.2008.02.025 Marri, 2018, Moments of compound renewal sums with dependent risks using mixing exponential models, Risks, 6, 86, 10.3390/risks6030086 Oakes, 1989, Bivariate survival models induced by frailties, Journal of the American Statistical Association, 84, 487, 10.1080/01621459.1989.10478795 Rider, 1962, The negative binomial distribution and the incomplete beta function, The American Mathematical Monthly, 69, 302, 10.2307/2312952 Salmon, 2006, Pricing multivariate currency options with copulas Sancetta, 2004, The Bernstein copula and its applications to modeling and approximations of multivariate distributions, Econometric Theory, 20, 535, 10.1017/S026646660420305X Sarabia, 2016, Risk aggregation in multivariate dependent Pareto distributions, Insurance. Mathematics & Economics, 71, 154, 10.1016/j.insmatheco.2016.07.009 Sarabia, 2018, Aggregation of dependent risks in mixtures of exponential distributions and extensions, ASTIN Bulletin, 48, 1079, 10.1017/asb.2018.13 Sklar, 1959, Fonctions de répartition à n dimensions et leurs marges, Publications de L'Institut de Statistique de L'Université de Paris, 8, 229 Spiegel, 2013 Tavin, 2013