On the drawdown of completely asymmetric Lévy processes
The drawdown process Y of a completely asymmetric Lévy process X is equal to X reflected at its running supremum X¯: Y=X¯−X. In this paper we explicitly express in terms of the scale function and the Lévy measure of X the law of the sextuple of the first-passage time of Y over the level a>0, the time G¯τa of the last supremum of X prior to τa, the infimum X¯τa and supremum X¯τa of X at τa and the undershoot a−Yτa− and overshoot Yτa−a of Y at τa. As application we obtain explicit expressions for the laws of a number of functionals of drawdowns and rallies in a completely asymmetric exponential Lévy model.
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Volume (Year): 122 (2012)
Issue (Month): 11 ()
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