Extremal behavior of stochastic integrals driven by regularly varying L\'{e}vy processes

Henrik Hult; Filip Lindskog

doi:10.1214/009117906000000548

Extremal behavior of stochastic integrals driven by regularly varying L\'{e}vy processes

Probability 2007-05-23 v1

Authors: Henrik Hult , Filip Lindskog

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Abstract

We study the extremal behavior of a stochastic integral driven by a multivariate L\'{e}vy process that is regularly varying with index $\alpha>0$ . For predictable integrands with a finite $(\alpha+\delta)$ -moment, for some $\delta>0$ , we show that the extremal behavior of the stochastic integral is due to one big jump of the driving L\'{e}vy process and we determine its limit measure associated with regular variation on the space of c\`{a}dl\`{a}g functions.

Keywords

lévy processes extreme value theory stochastic processes

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@article{arxiv.math/0703802,
  title  = {Extremal behavior of stochastic integrals driven by regularly varying L\'{e}vy processes},
  author = {Henrik Hult and Filip Lindskog},
  journal= {arXiv preprint arXiv:math/0703802},
  year   = {2007}
}

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Published at http://dx.doi.org/10.1214/009117906000000548 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Extremal behavior of stochastic integrals driven by regularly varying L\'{e}vy processes

Abstract

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