Ruin probability with claims modeled by a stationary ergodic stable process

T. Mikosch, G. Samorodnitsky

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    31 Citations (Scopus)
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    Abstract

    For a random walk with negative drift we study the exceedance probability (ruin probability) of a high threshold. The steps of this walk (claim sizes) constitute a stationary ergodic stable process. We study how ruin occurs in this situation and evaluate the asymptotic behavior of the ruin probability for a large variety of stationary ergodic stable processes. Our findings show that the order of magnitude of the ruin probability varies significantly from one model to another. In particular, ruin becomes much more likely when the claim sizes exhibit long-range dependence. The proofs exploit large deviation techniques for sums of dependent stable random variables and the series representation of a stable process as a function of a Poisson process.
    Original languageEnglish
    Pages (from-to)1814-1851
    JournalThe Annals of Probability
    Volume28
    Issue number4
    DOIs
    Publication statusPublished - 2000

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