caa a22 4500 605521697 CHVBK 20210128100741.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s10958-015-2229-4 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2229-4 Convergence of Insurance Payout Stochastic Processes to Generalized Poisson Process [Elektronische Daten] [A. Chuprunov, E. Permyakova] 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. Springer Science+Business Media New York, 2015 Chuprunov A. Kazan (Volga Region) Federal University, Kazan', Russia aut Permyakova E. Kazan (Volga Region) Federal University, Kazan', Russia aut Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 205/1(2015-02-01), 55-67 1072-3374 205:1<55 2015 205 10958 https://doi.org/10.1007/s10958-015-2229-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2229-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chuprunov A. Kazan (Volga Region) Federal University, Kazan', Russia aut NATIONALLICENCE 700 1- Permyakova E. Kazan (Volga Region) Federal University, Kazan', Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 205/1(2015-02-01), 55-67 1072-3374 205:1<55 2015 205 10958