tel-00703797, version 2 - 7 Jun 2012 Chapitre 4. Asymptotiques <strong>de</strong> la probabilité <strong>de</strong> ruine Centeno, M. d. L. (2002b), ‘Measuring the effects of reinsurance by the adjustment coefficient in the Sparre An<strong>de</strong>rson mo<strong>de</strong>l’, Insurance: Mathematics and Economics 30(1), 37–49. 174 Channouf, N. and L’Ecuyer, P. (2009), Fitting a normal copula for a multivariate distribution with both discrete and continuous marginals, in ‘Proceedings of the 2009 Winter Simulation Conference’. 205 Chaudry, M. A. and Zubair, S. M. (1994), ‘Generalized incomplete gamma functions with applications’, Journal of Computational and Applied Mathematics 55(1), 99–123. 177, 210 Chaudry, M. A. and Zubair, S. M. (2002), On a Class of Incomplete Gamma Functions with Applications, Chapman & Hall. 177, 207, 210 Clarke, F. H. and Bessis, D. N. (1999), ‘Partial subdifferentials, <strong>de</strong>rivates and Ra<strong>de</strong>macher’s theorem’, Transactions of the American Mathematical Society 351(7), 2899–2926. 211 Collamore, J. (1996), ‘Hitting probabilities and large <strong>de</strong>viations’, The Annals of Probability 24(4), 2065–2078. 174 Constantinescu, C., Hashorva, E. and Ji, L. (2011), ‘Archime<strong>de</strong>an copulas in finite and infinite dimensions—with application to ruin problems’, Insurance: Mathematics and Economics 49(3), 487–495. 174 Denuit, M. and Lambert, P. (2005), ‘Constraints on concordance measures in bivariate discrete data’, Journal of Multivariate Analysis 93, 40–57. 201 Dutang, C., Lefèvre, C. and Loisel, S. (2012), A new asymptotic rule for the ultimate ruin probability. Working paper, ISFA. 173 Embrechts, P. and Veraverbeke, N. (1982), ‘Estimates for the probability of ruin with special emphasis on the possibility of large claims’, Insurance: Mathematics and Economics 1(1), 55–72. 174 Flajolet, P. and Sedgewick, R. (1995), ‘Mellin transforms and asymptotics: Finite differences and Rice’s integrals’, Theoretical Computer Science 144(1-2), 101–124. 192, 193, 194 Fousse, L., Hanrot, G., Lefèvre, V., Pélissier, P. and Zimmermann, P. (2007), ‘MPFR: A multiple-precision binary floating-point library with correct rounding’, ACM Trans. Math. Softw. 33(2). 195 Fousse, L., Hanrot, G., Lefèvre, V., Pélissier, P. and Zimmermann, P. (2011), MPFR: A multiple-precision binary floating-point library with correct rounding. URL: http://mpfr.org/ 195 Frees, E. W. and Wang, P. (2006), ‘Copula credibility for aggregate loss mo<strong>de</strong>ls’, Insurance: Mathematics and Economics 38, 360–373. 205 Genest, C. and Neslehova, J. (2007), ‘A primer on copulas for count data’, ASTIN Bulletin . 196, 201 Gerber, H. U. (1988), ‘Mathematical fun with compound binomial process’, ASTIN Bulletin 18(2), 161–168. 177 212
tel-00703797, version 2 - 7 Jun 2012 BIBLIOGRAPHY Gerber, H. U. and Shiu, E. S. (1998), ‘On the time value of ruin’, North American Actuarial Journal 2(1), 48–78. 174 Gerber, H. U. and Shiu, E. S. (2005), ‘The time value of ruin in a Sparre An<strong>de</strong>rsen mo<strong>de</strong>l’, North American Actuarial Journal 9(2), 49–84. 174 Gordon, R. A. (1994), The Integrals of Lebesgue, Denjoy, Perron and Henstock, Vol. 4, American Mathematical Society. 210 Grandlund Torbjoern & the GMP Devel. Team (2011), GNU MP - The GNU Multiple Precision Arithmetic Library. URL: http://gmplib.org/ 195 Heil, C. (2007), ‘Real analysis lecture notes: absolute continuous and singular functions’, Lecture Notes, School of Mathematics, Georgia Institute of Technology. 183 Hil<strong>de</strong>brandt, T. (1971), Introduction to the Theory of Integration, Routledge. 183, 210 Huang, H.-N., Marcantognini, S. and Young, N. (2006), ‘Chain rules for higher <strong>de</strong>rivatives’, The Mathematical Intelligencer 28(2), 61–69. 188 Jeffrey, A. and Dai, H.-H. (2008), Handbook of Mathematical Formulas and Integrals, Aca<strong>de</strong>mic Press. 184 Joe, H. (1997), Multivariate <strong>de</strong>pen<strong>de</strong>nce measure and data analysis, in ‘Monographs on Statistics and Applied Probability’, Vol. 73, Chapman & Hall. 196, 205 Johnson, N. L., Kotz, S. and Kemp, A. W. (2005), Univariate Discrete Distributions, 3rd edn, Wiley Interscience. 208 Jones, D. S. (1997), Introduction to Asymptotics: a Treatment using Nonstandard Analysis, World Scientific. 181 Klueppelberg, C. and Stadtmueller, U. (1998), ‘Ruin probabilities in the presence of heavytails and interest rates’, Scandinavian Actuarial Journal 1998(1), 49–58. 174 Leon, A. R. D. and Wu, B. (2010), ‘Copula-based regression mo<strong>de</strong>ls for a bivariate mixed discrete and continuous outcome’, Statistics in Medicine . 205 Li, S., Lu, Y. and Garrido, J. (2009), ‘A re<strong>vie</strong>w of discrete-time risk mo<strong>de</strong>ls’, Revista <strong>de</strong> la Real Aca<strong>de</strong>mia <strong>de</strong> Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas 103(2), 321–337. 174 Lu, Y. and Garrido, J. (2005), ‘Doubly periodic <strong>non</strong>-homogeneous Poisson mo<strong>de</strong>ls for hurricane data’, Statistical Methodology 2(1), 17–35. 174 Maechler, M. (2012), Rmpfr: R MPFR - Multiple Precision Floating-Point Reliable, ETH Zurich. 195 Merentes, N. (1991), ‘On the Composition Operator in AC[a,b]’, Collect. Math. 42(3), 237– 243. 187 Nelsen, R. B. (2006), An Introduction to Copulas, Springer. 196, 197, 201 213
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