Far Eastern Mathematical Journal

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Continuity theorems and algorithmical problems in classical risk model

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

2010, issue 2, P. 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

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