Far Eastern Mathematical Journal

To content of the issue

Continuity theorems and algorithmical problems in classical risk model

T. A. Kalmykova, Yu. N. Kharchenko, G. Sh. Tsitsiashvili

2010, issue 2, Ñ. 153–161

In this paper an analog of the Bernstein theorem about an approximation of a probability distribution by a mixture of exponential distribution is proved in the metric $L_1$. Different generalizations of classical risk model on a case of dependent financial and insurance risks are constructed. In this case a possibility of a paralleling of algorithms of ruin probability calculation is analyzed.

classical risk model, ruin probability, mixtures of exponential distributions

Download the article (PDF-file)


[1] G. Sh. Ciciashvili, “Vychislenie veroyatnosti razoreniya v klassicheskoj modeli riska”, Avtomatika i telemexanika, 2009, ¹ 12, 187–194.
[2] R. Norberg, “Ruin problems with assets and liabilities of diffusion type”, Stochastic Process. Appl., 81:2 (1999), 255–269.
[3] Q. Tang, G. Tsitsiashvili, “Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks”, Stochast. Process. Appl., 108:2 (2003), 299–325.
[4] V. M. Zolotarev, “Stoxasticheskaya nepreryvnost' sistem massovogo obsluzhivaniya”, Teoriya veroyatnostej i ee primeneniya, 21:2 (1976), 260–279.
[5] A. Feldmann, W. Whitt, “Fitting mixtures of exponentials to long-tailed distributions to analyze network perfomance models”, Perfomance Evaluation, 31 (1998), 245–279.
[6] D. Dufresne, “Stochastic life annuities abstract”, American Actuarial Journal, 11:1 (2007), 136–157.
[7] B. Ko, A. C. Y. Ng, “Stochastic Annuities”, Daniel Dufresne, Discussions of papers already published, American Actuarial Journal, 11:3 (2007), 170–171.

To content of the issue