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The Tail Probability of Discounted Sums of Pareto-like Losses in Insurance |
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| Authors: | Marc J. Goovaerts Rob Kaas Qihe Tang Raluca Vernic |
| Affiliation: | 1. Department of Quantitative Economics , University of Amsterdam , Roetersstraat 11, 1018 WB, Amsterdam, The Netherlands;2. Center for Risk and Insurance Studies , Catholic University of Leuven , Naamsestraat 69, B-3000, Leuven, Belgium;3. Department of Quantitative Economics , University of Amsterdam , Roetersstraat 11, 1018 WB, Amsterdam, The Netherlands;4. Department of Mathematics and Statistics , Concordia University , 7141 Sherbrooke Street West, Montreal, Quebec, H4B 1R6, Canada;5. Faculty of Mathematics and Computer Science , Ovidius University of Constanta , 124 Mamaia Blvd, Constanta, Romania |
| Abstract: | In an insurance context, the discounted sum of losses within a finite or infinite time period can be described as a randomly weighted sum of a sequence of independent random variables. These independent random variables represent the amounts of losses in successive development years, while the weights represent the stochastic discount factors. In this paper, we investigate the problem of approximating the tail probability of this weighted sum in the case when the losses have Pareto-like distributions and the discount factors are mutually dependent. We also give some simulation results. |
| Keywords: | Asymptotics (Log)elliptical distribution (Log)normal variance-mean mixed distribution Pareto-like distribution Tail probability |