# Drawdowns and Rallies in a Finite Time-horizon

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DOI: 10.1007/s11009-009-9139-1

- Cite this article as:
- Zhang, H. & Hadjiliadis, O. Methodol Comput Appl Probab (2010) 12: 293. doi:10.1007/s11009-009-9139-1

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## Abstract

In this work we derive the probability that a rally of *a* units precedes a drawdown of equal units in a random walk model and its continuous equivalent, a Brownian motion model in the presence of a finite time-horizon. A rally is defined as the difference of the present value of the holdings of an investor and its historical minimum, while the drawdown is defined as the difference of the historical maximum and its present value. We discuss applications of these results in finance and in particular risk management.