Abstract
In this paper the ruin probability of the sum of two classical risk processes is studied under the assumption that the claim size distributions are of phase type and that the two Poisson processes of claim arrivals are correlated. The correlation between two claim number processes is modeled by Common Shock Model. We represent the merged risk process as a classical compound Poisson risk process where the initial claim size distributions are replaced by a new, properly chosen phase type distribution. This allows to construct an exact formula for the ruin probability of the merged risk process.
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References
Anastasiadis, S., Chukova, S.: Multivariate insurance models. An overview. Insur. Math. Econ. 51, 222–227 (2012)
Asmussen, S., Albrecher, H.: Ruin Probabilities, 2nd edn. World Scientific, New Jersey (2010)
Bäuerle, N., Grübel, R.: Multivariate risk processes with interacting intensities. Adv. Appl. Probab. 40, 578–601 (2008)
Cai, J., Li, H.: Dependence properties and bounds for ruin probabilities in multivariate compound risk models. J. Multivariate Anal. 98, 757–773 (2007)
Cai, J., Li, H.: Multivariate risk model of phase-type. Insur. Math. Econ. 36, 137–152 (2005)
Crámer, H.: On the Mathematical Theory of Risk. Skandia Jubilee Volume, Stockholm (1930)
Kreinin, A.: Financial Signal Processing and Machine Learning. J. Wiley & Sons (2016)
Lundberg, F.: I Approximerad Framställning av Sannolikhetsfunktionen. II Återförsäkring av Kollektivrisker. Almquist & Wiksell, Uppsala (1903)
Neuts, M.F.: Matrix-Geometric Solutions in Stochastic Models. John Hopkins University Press, Baltimore (1981)
Yuen, K. C., Guo, J., Wu, X.: On the first time of ruin in the bivariate compound Poisson model. Insur. Math. Econ. 38, 298–308 (2006)
Yuen, K. C., Guo, J., Wu, X.: On a correlated aggregate claims model with Poisson and Erlang risk processes. Insur. Math. Econ. 32, 205–214 (2002)
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Ali, M.J., Pärna, K. (2022). Ruin Probability for Merged Risk Processes with Correlated Arrivals. In: Malyarenko, A., Ni, Y., Rančić, M., Silvestrov, S. (eds) Stochastic Processes, Statistical Methods, and Engineering Mathematics . SPAS 2019. Springer Proceedings in Mathematics & Statistics, vol 408. Springer, Cham. https://doi.org/10.1007/978-3-031-17820-7_2
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DOI: https://doi.org/10.1007/978-3-031-17820-7_2
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