Ruin Probabilities for Two Risk Models with Asymptotically Independent and Dependent Classes

Document Type : Original Article

Author
Abouzar Bazyari
Department of Statistics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr, Iran. Department of Mathematics‎, ‎Salman Farsi University of Kazerun‎, ‎Kazerun‎, ‎Iran.
10.22034/jirss.2022.707215
Abstract
This paper presents two new insurance risk models for analyzing the ruin probabilities. Firstly, we restrict ourselves to the classical risk model contains heavy-tailed distribution of individual net losses and changeable premium income rates. Under certain technical assumptions, some asymptotic expansions and recursive formulas are obtained for the ruin probabilities. In the second risk model, we assume that the different classes of the portfolio business are dependent and compute the finite time ruin probability based on the discretization of the distribution function. We present some numerical examples in the portfolio of business and show that the value of ruin probability increases as dependence level increases. Moreover, the sensitivity of the results are investigated with respect to the parameters of  Weibull and Exponential distributions.
Keywords
Classical risk model
Dependence structure
Fourier transform method
Heavy-tailed distribution
Ruin probability
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Journal of the Iranian Statistical Society
Volume 21, Issue 2
December 2022
Pages 165-196

  • Receive Date 13 December 2019
  • Revise Date 10 June 2023
  • Accept Date 22 August 2023