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March 2015 Occupation times, drawdowns, and drawups for one-dimensional regular diffusions
Hongzhong Zhang
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Adv. in Appl. Probab. 47(1): 210-230 (March 2015). DOI: 10.1239/aap/1427814588

Abstract

The drawdown process of a one-dimensional regular diffusion process X is given by X reflected at its running maximum. The drawup process is given by X reflected at its running minimum. We calculate the probability that a drawdown precedes a drawup in an exponential time-horizon. We then study the law of the occupation times of the drawdown process and the drawup process. These results are applied to address problems in risk analysis and for option pricing of the drawdown process. Finally, we present examples of Brownian motion with drift and three-dimensional Bessel processes, where we prove an identity in law.

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Hongzhong Zhang. "Occupation times, drawdowns, and drawups for one-dimensional regular diffusions." Adv. in Appl. Probab. 47 (1) 210 - 230, March 2015. https://doi.org/10.1239/aap/1427814588

Information

Published: March 2015
First available in Project Euclid: 31 March 2015

zbMATH: 1310.60114
MathSciNet: MR3327322
Digital Object Identifier: 10.1239/aap/1427814588

Subjects:
Primary: 60J60
Secondary: 60G17

Rights: Copyright © 2015 Applied Probability Trust

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Vol.47 • No. 1 • March 2015
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