The probability and severity of ruin for combinations of exponential claim amount distributions and their translations |
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| Institution: | 1. Department of Mathematics, Abhedananda Mahavidyalaya, Sainthia, Birbhum 731234, West Bengal, India;2. Department of Mathematics, Sundarban Hazi Desarat College, Pathankhali, 743611 West Bengal, India;3. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur (Formerly, Bengal Engineering and Science University, Shibpur), Howrah 711103, West Bengal, India;1. UNESCO-IHE Institute for Water Education, Delft, the Netherlands;2. Water Resources Section, Delft University of Technology, Delft, the Netherlands;3. Hydrology and Quantitative Water Management Group, Wageningen University, Wageningen, The Netherlands;1. IHE Delft Institute for Water Education, Hydroinformatics Chair group, Delft, 2601 DA, the Netherlands;2. Delft University of Technology, Water Resources Section, Delft, the Netherlands;3. Hydrology and Quantitative Water Management Group, Wageningen University, Wageningen, the Netherlands;4. Water Problems Institute of the Russian Academy of Sciences, Moscow, Russia;5. School of Environmental Engineering, Technical University of Crete, Chania, Greece |
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| Abstract: | In the classical compound Poisson model of the collective theory of risk let ψ(u, y) denote the probability that ruin occurs and that the negative surplus at the time of ruin is less than − y. It is shown how this function, which also measures the severity of ruin, can be calculated if the claim amount distribution is a translation of a combination of exponential distributions. Furthermore, these results can be applied to a certain discrete time model. |
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