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EXTENSION OF THE SPARRE ANDERSEN RISK MODEL VIA THE SPEARMAN COPULA
Keywords:
Gerber-Shiu functions, dependence, copula, integro-differential equation, Laplace transformation, probability of failureDOI:
https://doi.org/10.17654/0972361723017Abstract
This paper is devoted to an extension of the Sparre Andersen risk model without the assumption of independence of claim amounts and time between claims. The dependent structure between these random variables is described by the Spearman copula. We study the Laplace transform of the discounted penalty function and the Laplace transform of the probability of the ruin.
Received: January 28, 2023; Accepted: March 1, 2023; Published: March 13, 2023
References
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.
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.
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.
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.
D. C. M. Dickson and C. Hipp, On the time to ruin for Erlang(2) risk process, Insurance Math. Econom. 29 (2001), 333-344.
H. U. Gerber and E. S. W. Shiu, On the time value of ruin, North American Actuarial Journal (1998), 48-78.
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.
R. B. Nelsen, An introduction to copulas, Springer Series in Statistics, 2nd ed., Springer-Verlag, New York, 2006.
H. Joe, Multivariate Models and Dependence Concepts, Chapman & Hall/CRC, 1997.
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.
W. Hürlimann, Multivariate Frechet copulas and conditional value-at-risk, Int. J. Math. Math. Sci. 7 (2004a), 345-364.
G. E. Wilmot, On the discounted penalty function in the renewal risk model with general interclaim times, Insurance Math. Econom. 41 (2007), 17-31.
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.
Cong Gu, The ruin problem of dependent risk model based on copula function, Journal of Chemical and Pharmaceutical Research 5(9) (2013), 234-240.
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.
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