Leaky faults provide important flow paths for fluids to move underground. It is often necessary to characterize such faults in engineering projects such as deep well injection of waste liquids, underground natural gas storage, and radioactive waste isolation. To provide this characterization, analytical solutions are presented for groundwater flow through saturated aquifer-fault-aquifer systems...

We consider the portfolio choice problem for an investor interested in long-run growth optimality while facing drawdown constraints in a general continuous semimartingale model. The paper introduces the numéraire property through the notion of expected relative return and shows that drawdown-constrained strategies with the numéraire property exist and are unique, but may depend on the financial...

A new distance-drawdown method for aquifers with anisotropy on the horizontal plane is presented. The method uses scalar transformation to convert to an equivalent, isotropic medium, thus permitting application of the Cooper-Jacob Method. The method is applicable to cases where at least one ellipse of equal drawdown can be delineated but can also be applied where no ellipse can be discerned fro...

Beijing is located on multiple alluvial-pluvial fans with thick Quaternary unconsolidated sediments. It has suffered serious groundwater drawdown and land subsidence due to groundwater exploitation. This study aimed to introduce geographical distribution measure methods into land subsidence research characterizing, geographically, land subsidence, groundwater drawdown, and compressible layer th...

Maximum Relative Drawdown measures the largest percentage drop of the price process on a given time interval. More 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 theoret...

[1] A semianalytical solution is presented for a mathematical model describing the flow of groundwater in response to a slug or pumping test in a highly permeable, confined aquifer. This solution, which is appropriate for wells of any degree of penetration and incorporates inertial mechanisms at both the test and observation wells, can be used to gain new insights into hydraulic tests in highly...

In this article, we define new “Greeks” for financial derivatives: sensitivities to the running maximum and the running maximum drawdown of an underlying asset. Some types of portfolios, such as the net asset value of a hedge fund or performance fees are sensitive to these parameters. In order to illustrate the concept of the new “Greeks”, we derive probabilistic representations of sensitivitie...

It has been hypothesized that changes in the marine biological pump caused a major portion of the glacial reduction of atmospheric carbon dioxide by 80 to 100 parts per million through increased iron fertilization of marine plankton, increased ocean nutrient content or utilization, or shifts in dominant plankton types. We analyze sedimentary records of marine productivity at the peak and the mi...

This paper studies drawdown and drawup processes in a general diffusion model. The main result is a formula for the joint distribution of the running minimum and the running maximum of the process stopped at the time of the first drop of size a. As a consequence, we obtain the probabilities that a drawdown of size a precedes a drawup of size b and vice versa. The results are applied to several ...