Far Eastern Mathematical Journal

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Numerical estimations of probability of the ruin in the classical model of the risk with constant interest in the case of heavy tails

E. S. Skvarnik

2004, issue 1, Ñ. 72–81

Classical risk model under constant interest is considered. Fast algorithms of its ruin probability calculation are suggested. Large differences between accuracy numerical meanings of ruin probabiity and its asymptotic are established for mean values of initial capital.

classical risk model, ruin probability, constant interest force

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[1] P. Embrechts, N. Veraverbeke, “Estimates for the probability of ruin with special emphasis on the possibility of large claims”, Insurance: Mathematics and Economics, 1 (1982), 55–72.
[2] S. Asmussen, “Subexponential asymptotics for stochastic processes: extremal behaviour, stationary distributions and first passage probabilities”, The Annals of Applied Probability, 8 (1998), 354–374.
[3] V. V. Kalashnikov, G. Sh. Tsitsiashvili, “Tails of waiting times and their bounds”, Queueing Systems, 32 (1999), 257–283.
[4] T. Mikosch, A. Nagaev, “Rates in approximations to ruin probabilities for heavy-tailed distributions”, Extremes, 4:1 (2001), 67–78.
[5] D. G. Konstantinides, Q. H. Tang, G. Sh. Tsitsiashvili, “Estimates for the ruin probability in the classical risk model with constant interest force in the presence of heavy tails”, Insurance: Mathematics and Economics, 31:3 (2002), 447–460.
[6] G. Sh. Ciciashvili, E. S. Skvarnik, Chislennoe reshenie zadachi o srednix znacheniyax v klassicheskoj modeli riska, Preprint IPM DVO RAN, Vladivostok, 2001, 11 s.

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