On the drawdown of completely asymmetric Levy processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Mijatovic, Aleksandar¹  Pistorius, Martijn R.^2,3 

[1] Univ Warwick, Dept Stat, Coventry CV4 7AL, W Midlands, England

[2] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

[3] Univ Amsterdam, Korteweg de Vries Inst Math, NL-1012 WX Amsterdam, Netherlands

关键词: Spectrally one-sided Levy process;    Reflected process;    Drawdown;    Fluctuation theory;    Excursion theory;    Sextuple law;   

DOI  :  10.1016/j.spa.2012.06.012

来源: Elsevier

【 摘 要 】

The drawdown process Y of a completely asymmetric Levy process X is equal to X reflected at its running supremum (X) over bar: Y = (X) over bar - X. In this paper we explicitly express in terms of the scale function and the Levy measure of X the law of the sextuple of the first-passage time of Y over the level a > 0, the time (G) over bar (tau a) of the last supremum of X prior to tau(a), the infimum (X) under bar (tau a) and supremum (X) over bar (tau a) of X at tau(a) and the undershoot a - Y tau a- overshoot Y-tau a - a of Y at tau(a). As application we obtain explicit expressions for the laws of a number of functionals of drawdowns and rallies in a completely asymmetric exponential Levy model. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

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