tunnelling through cities underlain by soft soil, commonly associated with soil movement around the tunnels and subsequent surface settlement. the predication of ground movement during the tunnelling and optimum support pressure could be based on analytical, empirical or the numerical methods. the commonly used earth pressure balance (epb) tunneling machines, uses the excavated soil in a pressu...

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...

A simplified model was employed to develop mathematically equations that describe the unsteadystate behavior of naturally fractured reservoirs, The analysis resulted in an equation of flow of radial symmetry whose solution, for the infinite case, is identical in form and function to that describing the unsteady-state behavior of homogeneous reservoirs. Accepting the assumed model, for all pract...

It has been observed that in the urban center of Shanghai, land subsidence has accelerated, and the groundwater level has continued to drop even though the net withdrawn volume (NWV) of groundwater has remained unchanged since 1980. An analysis of monitoring data shows that drawdown of the groundwater level is one of the factors that have influenced land subsidence since 1980. The NWV of ground...

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...