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In this work we derive analytical formulas for the joint distribution of the drawdown, the last visit time of the maximum of a process preceding the drawdown and the maximum of the process under general diffusion dynamics. The motivation for this work arises in the financial risk management of drawdowns.
Drawdowns measure the first time the current drop of an investor’s wealth from its historical maximum reaches a pre-specified level. Therefore a quantity related to the drawdown is the duration of time between the drawdown and the last time at which the maximum was achieved. This quantity is studied here.
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