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Sensitivity of the Stability Bound for Ruin Probabilities to Claim Distributions

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Abstract

We are interested in the approximation of the ruin probability of a classical risk model using the strong stability method. Particularly, we study the sensitivity of the stability bound for ruin probabilities of two risk models to approach (a simpler ideal model and a complex real one, which must be close in some sense) regarding to different large claims (heavy-tailed distributions). In a first case, we study the impact of the tail of some claim distributions on the quality of this approximation using the strong stability of a Markov chain. In a second case, we look at the sensitivity of the stability bound for the ruin probability regarding to different large claims, using two versions of the strong stability method: strong stability of a Markov chain and strong stability of a Lindley process. In both cases, comparative studies based on numerical examples and simulation results, involving different heavy-tailed distributions, are performed.

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Authors and Affiliations

  1. Research Unit LaMOS (Modeling and Optimization of Systems), University of Bejaia, Bejaia, 06000, Algeria

    Aicha Bareche & Mouloud Cherfaoui

  2. Department of Mathematics, University of Biskra, Biskra, 07000, Algeria

    Mouloud Cherfaoui

Authors
  1. Aicha Bareche
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  2. Mouloud Cherfaoui
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Correspondence to Aicha Bareche.

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Bareche, A., Cherfaoui, M. Sensitivity of the Stability Bound for Ruin Probabilities to Claim Distributions. Methodol Comput Appl Probab 21, 1259–1281 (2019). https://doi.org/10.1007/s11009-018-9675-7

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  • DOI: https://doi.org/10.1007/s11009-018-9675-7

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