In this paper we investigate a sequence of accurate approximations of ruin probabilities in discrete time models. We prove its convergence to the exact ruin probability without any restrictive assumptions on the claim distribution. Numerical studies show that the sequence, from the first term on, accurately approximates ruin probabilities. A formula for ruin probabilities in the finite horizon is also proposed.
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In the present paper we define Kantorovich variant of generalized Bernstein type rational functions. We establish the order of approximation for continuous functions in different normed spaces and also estimate the rate of convergence for functions of bounded variation.
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