On the drawdown of completely asymmetric Lévy processes

Aleksandar Mijatović and Martijn R. Pistorius

Stochastic Processes and their Applications, 2012, vol. 122, issue 11, 3812-3836

Abstract: 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.

Keywords: Spectrally one-sided Lévy process; Reflected process; Drawdown; Fluctuation theory; Excursion theory; Sextuple law (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (15)

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DOI: 10.1016/j.spa.2012.06.012

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