Extremal behavior of stochastic integrals driven by regularly varying L\'evy processes
Abstract
We study the extremal behavior of a stochastic integral driven by a multivariate L\'evy process that is regularly varying with index α>0. For predictable integrands with a finite (α+δ)-moment, for some δ>0, we show that the extremal behavior of the stochastic integral is due to one big jump of the driving L\'evy process and we determine its limit measure associated with regular variation on the space of c\`adl\`ag functions.
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