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On future drawdowns of Levy processes

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Title: On future drawdowns of Levy processes
Authors: Baurdoux, EJ
Palmowski, Z
Pistorius, MR
Item Type: Journal Article
Abstract: For a given Levy process X = ( X t ) t 2 R + and for xed s 2 R + [f1g and t 2 R + we analyse the future drawdown extremes that are de ned as follows: The path-functionals D t;s and D t;s are of interest in various areas of application, including nancial mathematics and queueing theory. In the case that X has a strictly positive mean, we nd the exact asymptotic decay as x ! 1 of the tail probabilities P ( D t < x ) and P ( D t < x ) of D t = lim s !1 D t;s and D t = lim s !1 D t;s both when the jumps satisfy the Cram er assumption and in a heavy-tailed case. Furthermore, in the case that the jumps of the L evy process X are of single sign and X is not subordinator, we identify the one-dimensional distributions in terms of the scale function of X . By way of example, we derive explicit results for the Black- Scholes-Samuelson model.
Issue Date: 3-Jan-2017
Date of Acceptance: 17-Dec-2016
URI: http://hdl.handle.net/10044/1/43333
DOI: https://dx.doi.org/10.1016/j.spa.2016.12.008
ISSN: 0304-4149
Publisher: Elsevier
Start Page: 2679
End Page: 2698
Journal / Book Title: Stochastic Processes and Their Applications
Volume: 127
Issue: 8
Copyright Statement: © 2017 Elsevier B.V. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Keywords: Statistics & Probability
0104 Statistics
1502 Banking, Finance And Investment
Publication Status: Published
Appears in Collections:Financial Mathematics
Faculty of Natural Sciences