The notion of drawdown is central to active portfolio management. Conditional Drawdown-at-Risk (CDaR) is defined as the average of a specified percentage of the largest drawdowns over an investment horizon and includes maximum and average drawdowns as particular cases. The necessary optimality conditions for a portfolio optimization problem with CDaR yield the capital asset pricing model (CAPM)...

Maximum drawdown is a risk measure that plays an important role in portfolio management. In this paper, we address the question of computing the expected value of the maximum drawdown using a partial differential equation (PDE) approach. First, we derive a two-dimensional convection-diffusion pricing equation for the maximum drawdown in the Black-Scholes framework. Due to the properties of the ...

Within impounded sections of the rivers Rhine and Meuse, epibenthic macroinvertebrate communities are impoverished and dominated by non-native invasive species such as the zebra mussel (Dreissena polymorpha) and quagga mussel (Dreissena rostriformis bugensis). In the winter of 2012 management of the water-level resulted in a low-water event in the River Nederrijn, but not in the River Meuse. Lo...

A new one-parameter family of risk measures called Conditional Drawdown (CDD) has been proposed. These measures of risk are functionals of the portfolio drawdown (underwater) curve considered in active portfolio management. For some value of the tolerance parameter α, in the case of a single sample path, drawdown functional is defined as the mean of the worst (1 − α) ∗ 100% drawdowns. The CDD m...

In this article, we study the concept of maximum drawdown and its relevance to the prevention of portfolio losses. Maximum drawdown is defined as the largest market drop during a given time interval. We show that maximum drawdown can serve as an additional tool for portfolio managers on top of already existing contracts, such as put or lookback options.

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...

In the process of exploiting geothermal energy by groundwater heat pump, dynamic equilibrium regional drawdown is basis for sustained operation pump. this paper, taking pump project Fuyang People?s Hospital in Anhui, China as an example, a mathematical model established and numerical simulation carried out based on hydrogeological conceptual using MODFLOW software. addition, considering pattern...