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چکیده
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In theory, ruin probabilities in classical insurance risk models can be expressed in terms of an infinite sum of convolutions, but its inherent complexity makes efficient computation almost impossible. This paper aims to compute the ultimate time ruin probability in the classical insurance risk model using the defective renewal equation. Firstly, the defective renewal equation of model with compound geometric distribution is obtained, then according to this equation, the ultimate time ruin probability and ruin time moments are computed. To show the application of proposed method, we illustrate the problem for the Pareto distribution. The numerical evaluations and the first moment of the ruin time are evaluated and compared with Tang:2004, Wang and Yin:2010.
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