We consider stochastic processes describing the size of a company’s insurance payouts in the case of a growing number of clients. Convergence of such processes in Skorokhod space is proved. As a result, a functional limit theorem for risk processes is obtained, which allows us to use well-known formulas for estimating an insurance company’s ruin probability in the considered case.
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References
A. N. Shiryaev, Essentials of Stochastic Finance, World Scientific, Singapore (1999).
I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes, Dover Publications, New York (1996).
O. V. Rusakov, “Functional limit theorem for random variables with strong residual dependence,” Theory Probab. Appl., 40, No. 4, 813–832 (1995).
I. Fazekas and A. Chuprunov, Convergence of Random Step Lines to Ornstein-Uhlenbeck Type Processes, Technical Report of the Debrecen University, No. 24 (1996).
V.M. Kruglov and V.Yu. Korolev, Limit Theorems for Random Sums [in Russian], Izdat. MGU, Moscow (1990).
V. V. Kalashnikov, “Ruin probability,” Fund. i Prikl. Matem. [in Russian], 2, No. 4, 1055–1100 (1996).
V.E. Bening and V.Yu. Korolev, “Asymptotic decomposition of ruin probability in classical risk process under small security demand,” Obozrenie Prikl. i Promyshl. Matem. Ser. Financ. i Strakh. Matem. [in Russian], 7, No. 1, 177–179 (2000).
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Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, Vol. 19, pp. 149–168, 2006
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Chuprunov, A.N., Permyakova, E.E. Convergence of Insurance Payout Stochastic Processes to Generalized Poisson Process. J Math Sci 205, 55–67 (2015). https://doi.org/10.1007/s10958-015-2229-4
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DOI: https://doi.org/10.1007/s10958-015-2229-4