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Erlangian Approximation to Finite Time Ruin Probabilities in Perturbed Risk Models

Authors: Kaiqi Yu, David A. Stanford, and Jiandong Ren

Published in: Dagstuhl Seminar Proceedings, Volume 7461, Numerical Methods for Structured Markov Chains (2008)

Abstract

In this work-in-progress, we consider perturbed risk processes that have an underlying Markovian structure, including Markovian risk processes, and Sparre-Andersen risk processes when both inter claim times and claim sizes are phase-type. We apply the Erlangization method to this risk process in order to obtain an accurate approximation of the finite time ruin probability. In addition, we recognize a repeating structure in the probability matrices we work with. This is the key element in developing more efficent algorithms for the computation of the ruin probabilities. Several numerical examples are present to illustrate the model.

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Kaiqi Yu, David A. Stanford, and Jiandong Ren. Erlangian Approximation to Finite Time Ruin Probabilities in Perturbed Risk Models. In Numerical Methods for Structured Markov Chains. Dagstuhl Seminar Proceedings, Volume 7461, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{yu_et_al:DagSemProc.07461.6,
  author =	{Yu, Kaiqi and Stanford, David A. and Ren, Jiandong},
  title =	{{Erlangian Approximation to Finite Time Ruin Probabilities in Perturbed Risk Models}},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  pages =	{1--15},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7461},
  editor =	{Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and Marie-Ange Remiche and Peter Taylor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07461.6},
  URN =		{urn:nbn:de:0030-drops-13999},
  doi =		{10.4230/DagSemProc.07461.6},
  annote =	{Keywords: Perturbed risk processes, finite-time ruin probability, phase-type distribution, fluid flow models, Erlangization}
}

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Erlangian Approximation to Finite Time Ruin Probabilities in Perturbed Risk Models

Abstract

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