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• W2059423650 abstract "In this paper, we propose a class of infinite-dimensional phase-type distributions with finitely many parameters as models for heavy tailed distributions. The class of finite-dimensional phase-type distributions is dense in the class of distributions on the positive reals and may hence approximate any such distribution. We prove that formulas from renewal theory, and with a particular attention to ruin probabilities, which are true for common phase-type distributions also hold true for the infinite-dimensional case. We provide algorithms for calculating functionals of interest such as the renewal density and the ruin probability. It might be of interest to approximate a given heavy tailed distribution of some other type by a distribution from the class of infinite-dimensional phase-type distributions and to this end we provide a calibration procedure which works for the approximation of distributions with a slowly varying tail. An example from risk theory, comparing ruin probabilities for a classical risk process with Pareto distributed claim sizes, is presented and exact known ruin probabilities for the Pareto case are compared to the ones obtained by approximating by an infinite-dimensional hyper-exponential distribution." @default.
• W2059423650 created "2016-06-24" @default.
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• W2059423650 date "2014-01-15" @default.
• W2059423650 modified "2023-10-16" @default.
• W2059423650 title "Calculation of ruin probabilities for a dense class of heavy tailed distributions" @default.
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• W2059423650 doi "https://doi.org/10.1080/03461238.2013.865257" @default.
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