Abstract
The Cramer–Lundberg model is considered as a model of insurance company. Since it is impossible to obtain an explicit solution for the non-ruin probability function of insurance company for an arbitrary distribution of the values of insurance claims, the authors consider the problem of estimating the convergence of the original non-ruin probability to one that would be obtained by approximating the values of claim distribution function.
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References
F. I. Lundberg, Approximerad Framstallning av Sannolikhetsfunktionen, II. Aterforsakring av Kollektivrisker, Almqvist & Wiksell, Uppsala (1903).
F. I. Lundberg, Forsakringsteknisk Riskutjamning, F. Englunds boktryckeri A. B., Stockholm (1926).
R. E. Beard, T. Pentikainen, and E. Pesonen, Risk Theory. The Stochastic Basis of Insurance, Chapman and Hall, London–New York (1984).
M. M. Leonenko, Yu. S. Mishura, V. M. Parkhomenko, and M. J. Yadrenko, Probability-Theoretic and Statistical Methods in Econometrics and Financial Mathematics [in Ukrainian], Informtekhnika, Kyiv (1995).
S. Assmussen and H. Albrecher, Ruin Probabilities, Advanced Series on Statistical Science & Applied Probability, Vol. 14, World Scientific, Singapore (2010).
B. V. Bondarev and T. V. Zhmykhova, “Insurance company’s non-ruin probability for the Cramer–Lundberg model and G-distributed claim,” Prykladna Statystyka. Aktuarna ta Finansova Matem., No. 1–2, 54–70 (2005).
B. V. Bondarev and V. O. Boldyreva, “Approximation of non-ruin probability for the Cramer-Lundberg model,” Prykladna Statystyka. Aktuarna ta Finansova Matem., No. 1, 13–22 (2012).
A. V. Tymko, “Approximation of the distribution of a positive random variable by a mixture of shifted exponential distributions,” Visnyk Donetsk. Univer., Ser. A: Pryrodnychi Nauky, Issue 1, 20–25 (2006).
V. O. Boldyreva, “Modeling and analysis of the activity of insurance companies on (B, S)-market,” Author’s Abstract of Ph.D. Theses, V. M. Glushkov Inst. of Cybernetics, NAS of Ukraine, Kyiv (2015).
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Translated from Kibernetika i Sistemnyi Analiz, No. 2, March–April, 2018, pp. 78–84.
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Boldyreva, V.O., Shevchenko, G.M. On the Continuous Dependence of Non-Ruin Probability on Claim Distribution Function in the Classical Risk Model. Cybern Syst Anal 54, 242–248 (2018). https://doi.org/10.1007/s10559-018-0025-0
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DOI: https://doi.org/10.1007/s10559-018-0025-0