Ruin related quantities in a class of state-space compound binomial models

Document Type : Original Scientific Paper

Author

Department of Statistics‎, ‎Faculty of Intelligent Systems Engineering and Data Science‎, ‎Persian Gulf University‎, ‎Bushehr‎, ‎Iran

Abstract

The main focus of this paper is to extend the analysis of some ruin related problems to a class of state-space compound binomial risk models for a sequence of independent and identically distributed random variables of interclaim times when the claim occurrences are homogeneous‎. ‎First‎, ‎we obtain the mass function of a defective renewal sequence of random {Fn }n≥0 -stopping times‎, ‎using the compound binomial of aggregate claim amount together the net profit condition‎, ‎and compute the infinite time ruin probability with Markov property of risk process‎. ‎Moreover‎, ‎we derive the distribution of the time to ruin among many random variables associated with ruin using the convolution of claim amount and Lagrange’s implicit function theorem‎. ‎Lastly‎, ‎the theoretical results are illustrated with numerical computations‎.

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Journal of Statistical Modelling: Theory and Applications
Volume 3, Issue 2
July 2022
Pages 51-70

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History

  • Receive Date: 07 October 2022
  • Revise Date: 22 June 2023
  • Accept Date: 23 June 2023

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