.svg){kind=logo}
EXTENSION OF THE COMPOUND POISSON MODEL VIA THE SPEARMAN COPULA
Keywords:
Gerber-Shiu functions, dependence, copula, integro-differential equation, Laplace transformation, probability of failure.DOI:
https://doi.org/10.17654/0972086323008Abstract
In this paper, we consider an extension of the classical risk model. In this contribution, a tail dependence structure between claim amounts and inter-loss times with a Brownian disturbance is introduced by the Spearman copula in order to evaluate the Gerber-Shiu functions and the loss probabilities associated with this model. We determine integro-differential equations for the Gerber-Shiu function from which expressions for the Laplace transforms of the time to ruin and the deficit to ruin are derived for claim amounts that obey an exponential law.
Received: April 11, 2023
Accepted: May 18, 2023
References
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.
H. U. Gerber and E. S. W. Shiu, On the time value of ruin, North Amer. Actuar. J. 2 (1998), 48-72.
R. B. Nelsen, An Introduction to Copulas, 2nd ed., Springer Series in Statistics, Springer-Verlag, New York, 2006.
S. Heilpern, Ruin measures for a compound Poisson risk model with dependence based on the Spearman copula and the exponential claim sizes, Insurance: Mathematics and Economics 59 (2014), 251-257.
Z. Zhang and H. Yang, Gerber-Shiu analysis in a perturbed risk model with dependence between claim sizes and interclaim times, J. Comput. Appl. Math. 235 (2011), 1189-1204.
Ivo Adan, On the application of Rouché’s theorem in queueing theory, Queueing Systems 87(3-4) (2017), 223-236.
V. Klimenok, On the modification of Rouche’s theorem for the queuing theory problems, Queuing Systems 38 (2001), 431-434.
Franck Adékambi and Essodina Takouda, Gerber-Shiu function in a class of delayed and perturbed risk model with dependence, Risks 8(1) (2020), 30.
https://doi.org/10.3390/risks8010030.
W. Hürlimann, Fitting bivariate cumulative returns with copulas, Comput. Statist. Data Anal. 45(2) (2004), 355-372.
A. K. Nikoloulopoulos and D. Karlis, Fitting copulas to bivariate earthquake data: the seismic gap hypothesis revisited, Environmetrics 19 (2008), 251-269.
A. N. Borodin and P. Salminen, Handbook of Brownian Motion - Facts and Formulae, 2nd ed., Birkhäuser-Verlag, 2002.
S. Asmussen, Stationary distributions for fluid flow models with or without Brownian noise, Communications in Statistics - Stochastic Models 11 (1995).
Z. Zhang and H. Yang, Ruin probabilities in a perturbed compound Poisson risk model with dependence, Insurance: Mathematics and Economics 44(2) (2009), 294-299.
Karim Ben Amara, Quelques méthodes pour la résolution des équations intégro-différentielles, mémoire de magistère, Université Kasdi Merbah Ouargla, 2015.
W. Hürlimann, Multivariate Frechet copulas and conditional value-at-risk, Int. J. Math. Math. Sci. 7 (2004), 345-364.
M. Boudreault, H. Cossette, D. Landriault and E. Marceau, On a risk model with dependence between interclaim arrivals and claim sizes, Scand. Actuar. J. 106(5) (2006), 301-323.
Downloads
Published
Issue
Section
License
Copyright (c) 2023 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA
This work is licensed under a Creative Commons Attribution 4.0 International License.
____________________________
Attribution: Credit Pusha Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pusha Publishing House for more info or permissions.
