Keywords and phrases: Gerber-Shiu functions, dependence, copula, integro-differential equation, Laplace transformation, probability of failure.
Received: January 28, 2023; Accepted: March 1, 2023; Published: March 13, 2023
How to cite this article: Delwendé Abdoul-Kabir Kafando, Victorien Konané, Frédéric Béré and Pierre Clovis Nitiéma, Extension of the Sparre Andersen risk model via the Spearman copula, Advances and Applications in Statistics 86(1) (2023), 79-100. http://dx.doi.org/10.17654/0972361723017
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] H. Albrecher and J. Teugels, On a risk model with dependence between interclaim arrivals and claim sizes, J. Appl. Probab. 43(1) (2006), 265-285. [2] M. Boudreault, H. Cossette, D. Landriault and E. Marcean, On a risk model with dependence between interclaim arrivals and claim sizes, Scand. Actuar. J. (2006), 301-323. [3] Y. B. Cheng and Q. H. Tang, A note on the severity of ruin in the renewal model with claims of dominated variation, North American Actuarial Journal 21 (2003), 1-12. [4] H. Cossette, E. Marceau and F. Marri, On the compound Poisson risk model with dependence based on a generalized Farlie-Gumbel-Morgenstern copula. Insurance Math. Econom. 43(3) (2008), 444-455. [5] D. C. M. Dickson and C. Hipp, On the time to ruin for Erlang(2) risk process, Insurance Math. Econom. 29 (2001), 333-344. [6] H. U. Gerber and E. S. W. Shiu, On the time value of ruin, North American Actuarial Journal (1998), 48-78. [7] S. Heilpern, Ruin measures for a compound Poisson risk model with dependence based on the Spearman copula and the exponential claim sizes, Insurance Math. Econom. 59 (2014), 251-257. [8] R. B. Nelsen, An introduction to copulas, Springer Series in Statistics, 2nd ed., Springer-Verlag, New York, 2006. [9] H. Joe, Multivariate Models and Dependence Concepts, Chapman & Hall/CRC, 1997. [10] H. Cossette, E. Marceau and F. Marri, Analysis of ruin measures for the classical compound Poisson risk model with dependence, Scand. Actuar. J. 3 (2010), 221-245. [11] W. Hürlimann, Multivariate Frechet copulas and conditional value-at-risk, Int. J. Math. Math. Sci. 7 (2004a), 345-364. [12] G. E. Wilmot, On the discounted penalty function in the renewal risk model with general interclaim times, Insurance Math. Econom. 41 (2007), 17-31. [13] C. K. Cheung, D. Landriault, G. E. Willmot and J.-K. Woo, Structural properties of Gerber-Shiu functions in dependent Sparre Andersen models, Insurance Math. Econom. 46 (2010), 117-126. [14] Cong Gu, The ruin problem of dependent risk model based on copula function, Journal of Chemical and Pharmaceutical Research 5(9) (2013), 234-240. [15] Olena Ragulina, The risk model with stochastic premiums, dependence and a threshold dividend strategy, Journal of Modern Stochastics: Theory and Applications 4(4) (2017), 315-351.
|