Conditional value-at-risk

Figure 7.2 Pareto front and compromise decisions. Vertical line is naive approach. CVaR, conditional-value-at-risk.

Tyrrell RockafeUar R, Uryasev S. Optimization of conditional value-at-risk. J Risk 2000 2 21-42. 

Conditional value at risk CVaR, CVaR, = [ VaR dM Ja Area under the EP curve below a selected cumulative probability level a, normalized by the exceedance probability 1—a... 

Duarte also proposes a generalized approach to asset allocation that includes mean semi-variance, mean absolute deviation, MV, and value-at-risk as special cases. While cleverly broad, Duarte s method relies on simulation teclmiques and is computationally burdensome. In addition, because simulation approaches do not have explicit analytical solutions, the technique loses some of the precision of MV analysis. For example, one can examine solution sensitivities from the second-order conditions of MV problems, but this is not so easy with the simulation. It remains to be seen whether simulation approaches receive widespread acceptance for solving portfolio problems. Nonetheless, simulation techniques offer tremendous potential for future applications. 

It is current medical practice to select the weighting factors as a function of two main criteria (1) late tolerance in normal tissues and (2) in relation to a daily fractionation of 2 Gy (photons or Co-gamma rays). Therefore among the published RBE values, those obtained for late elfects on normal tissues, with 2 Gy of photons per fraction as reference, are the most relevant for the selection of the RBE weighting factor and could be defined as reference conditions. The reference RBE is then, to some extent, an average or overall RBE for late tolerance of normal tissues at risk, evaluated vs. 2 Gy per fraction of photon radiation. 

Problem formulation. Within this process all available information about a contaminated site is collected including the nature of the contaminants and their sources, obvious effects and potential receptors as well as environmental recipients. Within this very first stage of the risk assessment procedure, an assessment endpoint has to be determined. Assessment endpoints are the expression of an environmental value (represented by an ecological entity) that is at risk, e.g. a distinct population that faces harm due to pollution. It has to be emphasised that toxicity-test endpoints or other measurement endpoints (in general, measured effects under test conditions) in most cases do not represent assessment endpoints (response of population or ecosystem in the field). Measurement endpoints should be representative for assessment endpoints or have a known relationship to the assessment endpoint allowing the extrapolation of data. 

The presence of hypochlorous acid as opposed to the hypochlorite ion, is responsible for the biocidal activity. Hypochlorous acid is estimated to be twenty times more effective as a micro-biocide than the hypochlorite ion. Unfortunately however, in a cooling tower there is a tendency to strip chlorine from the water by the countercurrent flow of the air, so that Equation 14.23 moves to the left and it is likely that by the time the water reaches the basin of the tower all the chlorine will have been lost to the air in addition to reactions with organic matter within the tower. It will be necessary therefore for maximum utilisation of the available chlorine to ensure that the equilibrium of Equation 14.24, is over to the LHS. Since the ionisation process produces hydrogen ions the equilibrium will be affected by the pH of the solution. The effect of pH on HOCl stability is shown on Fig. 14.16 [Marshall and Bott 1988]. In the figure 100% HOCl indicates that the equilibrium is completely to the left in Equation 14.24 and there is no ionisation of the HOCl. From Fig. 14.16 this condition occurs at pH of around 5. At a pH 7.5 hypochlorite ion and acid co-exist in approximately equal amounts. It nll be seen that as the pH approaches 9 the hypochlorous acid content drops to a very low value and the biocidal effect is negligible. Values of pH lower than around 6.5 are not practical because of the potential risk of corrosion. 

Grade A The local zone for high risk operations, e.g., filling zone, stopper bowls, open ampoules and vials, making aseptic connections. Normally such conditions are provided by a laminar air flow work station. Laminar air flow systems should provide an homogeneous air speed of 0.45m/s +/-20% (guidance value) at the working position. 

Initial conditions defined at two points along the risk spectrum create so-called boundary value problems in that the solutions to the differential equations depend on the initial conditions but the initial conditions depend on the solutions to the differential equations. The least complicated method of solving boimdary value problems is to approximate the functions M(n), and W(7t) in equations (3.2),... 

However, there are no clear cut-off values for basic laboratory parameters, which could be useful for preselecting patients at risk of potential detrimental conditions. Some parameters that are easy to detect, such as lactic/pyruvic metabolic acidosis, are not specific for thiamine deficiency (Table 33.2). On the other hand, blood TDP and transketolase assays have low sensitivity due to significant overlapping results between healthy and thiamine-deficient individuals. This makes laboratory assessment of borderline thiamine deficiency conditions difficult. Thus, anamnesis and awareness of the socio-demographic conditions of the patient are as important as laboratory tests in the early diagnosis of thiamine deficiency. 

DFT can be done using any number of samples, but FFT requires that the number of values in the set be a power of 2 2,4,8, etc. If you can control the data acquisition, just acquire 2 values. If you are given a dataset that does not satisfy this condition, you must either discard some values at the end of the sequence, or pad the sequence with phony values - at the risk of introducing a step function that will contaminate the process. 

---