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October 2000 Ruin probability with claims modeled by a stationary ergodic stable process
Thomas Mikosch, Gennady Samorodnitsky
Ann. Probab. 28(4): 1814-1851 (October 2000). DOI: 10.1214/aop/1019160509


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.


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Thomas Mikosch. Gennady Samorodnitsky. "Ruin probability with claims modeled by a stationary ergodic stable process." Ann. Probab. 28 (4) 1814 - 1851, October 2000.


Published: October 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1044.60028
MathSciNet: MR1813844
Digital Object Identifier: 10.1214/aop/1019160509

Primary: 60E07
Secondary: 60G10 , 60K30

Keywords: heavy tails , negative drift , risk , ruin probability , Stable process , stationary process , supremum

Rights: Copyright © 2000 Institute of Mathematical Statistics

Vol.28 • No. 4 • October 2000
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