On the drawdown of completely asymmetric Levy processes

2011/03/08 by Aleksandar Mijatović, Mijatovic, Aleksandar, Martijn Pistorius +1 · 3 citations
Economics, Econometrics and Finance · #60G17 #60G51 #Complex Systems and Time Series Analysis #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Risk Management (q-fin.RM) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1103.1460

openalex publication_date 2011/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The \em 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 τ_a, the infimum \unl X_τa and supremum \ovl X_τa of X at τ_a and the undershoot a - Y_τa- and overshoot Y_τa-a of Y at τ_a. 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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