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Downside risk (DR) is measured by target semi-deviation (the square root of target semivariance) and is termed downside deviation. It is expressed in percentages and therefore allows for rankings in the same way as standard deviation. An intuitive way to view downside risk is the annualized standard deviation of returns below the target.
Downside risk was first modeled by Roy (1952), who assumed that an investor's goal was to minimize his/her risk. This mean-semivariance, or downside risk, model is also known as “safety-first” technique, and only looks at the lower standard deviations of expected returns which are the potential losses.
The ratio is calculated as =, where is the asset or portfolio average realized return, is the target or required rate of return for the investment strategy under consideration (originally called the minimum acceptable return MAR), and is the target semi-deviation (the square root of target semi-variance), termed downside deviation.
Examples of common classes of biological targets are proteins and nucleic acids. The definition is context-dependent, and can refer to the biological target of a pharmacologically active drug compound, the receptor target of a hormone (like insulin), or some other target of an external stimulus.
In financial mathematics, a deviation risk measure is a function to quantify financial risk (and not necessarily downside risk) in a different method than a general risk measure. Deviation risk measures generalize the concept of standard deviation .
Identify the model output to be analysed (the target of interest should ideally have a direct relation to the problem tackled by the model). Run the model a number of times using some design of experiments, [15] dictated by the method of choice and the input uncertainty. Using the resulting model outputs, calculate the sensitivity measures of ...
In the first example provided above, the sex of the patient would be a nuisance variable. For example, consider if the drug was a diet pill and the researchers wanted to test the effect of the diet pills on weight loss. The explanatory variable is the diet pill and the response variable is the amount of weight loss.
The optimal paths for the fastest can be found using the Wencell-Freidlin functional in the Large-deviation theory. These paths correspond to the short-time asymptotics of the diffusion equation from a source to a target. In general, the exact solution is hard to find, especially for a space containing various distribution of obstacles.