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Drawdowns and Rallies in a Finite Time-horizon

Hongzhong Zhang () and Olympia Hadjiliadis ()
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Hongzhong Zhang: C.U.N.Y.
Olympia Hadjiliadis: C.U.N.Y.

Methodology and Computing in Applied Probability, 2010, vol. 12, issue 2, 293-308

Abstract: 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.

Keywords: Drawdown; Rally; Random walk; Brownian motion; Primary 60G40; Secondary 91A60 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s11009-009-9139-1

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