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 appli...

A taxonomy of large financial crashes proposed in the literature locates the burst of speculative bubbles due to endogenous causes in the framework of extreme stock market crashes, defined as falls of market prices that are outlier with respect to the bulk of drawdown price movement distribution. This paper goes on deeper in the analysis providing a further characterization of the rising part o...

Maximum Relative Drawdown measures the largest percentage drop of the price process on a given time interval. Recently, Maximum Relative Drawdown has become more popular as an alternative measure of risk. In contrast to the Value at Risk measure, it captures the path property of the price process. In this article, we propose a partial differential equation approach to determine the theoretical ...

Maximum drawdown, the largest cumulative loss from peak to trough, is one of the most widely used indicators of risk in the fund management industry, but one of the least developed in the context of probabilistic risk metrics. We formalize drawdown risk as Conditional Expected Drawdown (CED), which is the tail mean of maximum drawdown distributions. We show that CED is a degree one positive hom...

Currently, type curve analysis methods are being commonly used in conjunction with the conventional methods to obtain better interpretation of well test data. Although the majority of published type curves are based on pressure drawdown solutions, they are often applied indiscriminately to analyze both pressure drawdown and buildup data. Moreover, the limitations of drawdown type curves, to ana...

Hydrological alternation can dramatically influence riparian environments and shape riparian vegetation zonation. However, it was difficult to predict the status in the drawdown area of the Three Gorges Reservoir (TGR), because the hydrological regime created by the dam involves both short periods of summer flooding and long-term winter impoundment for half a year. In order to examine the effec...

Dynamically allocating wealth between cash and a performance-seeking portfolio allows investors to limit drawdowns to a chosen pre-defined level or risk-budget. This paper introduces variants and generalizations of the maximum drawdown metric and the corresponding risk-control strategies, such as excess drawdown, relative drawdown, and rolling drawdowns control. We discuss the relevance of thes...

A drawdown constraint forces the current wealth to remain above a given function of its maximum to date. We consider the portfolio optimisation problem of maximising the long-term growth rate of the expected utility of wealth subject to a drawdown constraint, as in the original setup of Grossman and Zhou (1993). We work in an abstract semimartingale financial market model with a general class o...

The drawdown of an asset is a risk measure defined in terms of the running maximum of the asset’s spot price over some period [0, T ]. The asset price is said to have drawn down by at least $K over this period if there exists a time at which the underlying is at least $K below its maximum-to-date. We introduce insurance against a large realization of maximum drawdown and a novel way to hedge th...

The identification of spatial variations in hydraulic conductivity (K) on a scale of relevance for transport investigations has proven to be a considerable challenge. Recently, a new field method for the estimation of interwell variations in K has been proposed. This method, hydraulic tomography, essentially consists of a series of short-term pumping tests performed in a tomographic-like arrang...