Risk model

Tang, Z., Taylor, M. J., Lisboa, P., and Dyas, M. (2005). Quantitative risk modeling for new pharmaceutical compounds. Drug Disc Today 22 1 520-1526. 

It emphasises the need to research quantitative evaluation risk models and thus to provide for the reader means to define a level of danger, in a rigorous fashion, taking into account in his own way work already carried out in this domain. The model proposed ought to be considered as a route and a clue to a way of thinking and not necessarily as definitive. 

Poor Prognostic Factors (Sokal Risk Model)6... 

On July 18, 2000, the Agency released HWIR-waste exemption levels for 36 chemicals that were developed using a risk model known as the Multimedia, Multi-pathway and Multi-receptor Risk Assessment (3MRA) Model.17 The May 16, 2001, HWIR-waste rule revised and retained the hazardous waste mixture and derived-from rules as previously discussed in this module. In addition, the rule finalized provisions that conditionally exempt mixed waste (waste that is both radioactive and hazardous), if the mixed waste meets certain conditions in the rule.5... 

SADA provides a full human health risk assessment module and associated databases. The risk models follow the USEPA s Risk Assessment Guidance for Superfund (RAGS) and can be customized to fit site-specific exposure conditions. It calculates risks based on the following exposure pathways ingestion, inhalation, dermal contact, food consumption, and also a combined exposure. 

The relative risk model may be expressed in a simple form ... 

In this way it was possible to test the relative risk model. 

Haimes, Y. Y. 2004. Risk modeling, assessment, and management. 2nd ed. New York Wiley. 

Haimes, Y. (1998) Risk Modeling, Assessment, and Management. New York, John Wiley and Sons. 

For those substances for which appropriate human smdies are available, the so-called average relative risk model has been used. Quantitative assessments using this model comprises four steps (1) selection of studies (2) standardized description of study results in terms of relative risk, exposure level, and duration of exposure (3) extrapolation towards zero dose and (4) application to a general (hypothetical) population. 

Such a risk management framework should be in place prior to the initiation of closure activities and should be a dynamic process. The constituent risk models should be updated as new information becomes available and should be responsive to changing and emerging hazards. 

Consideration of the expected value of profit alone as the objective function, which is characteristic of the classical stochastic linear programs introduced by Dantzig (1955) and Beale (1955), is obviously inappropriate for moderate and high-risk decisions under uncertainty since most decision makers are risk averse in facing important decisions. The expected value objective ignores both the risk attribute of the decision maker and the distribution of the objective values. Hence, variance of each of the random price coefficients can be adopted as a viable risk measure of the objective function, which is the second major component of the MV approach adopted in Risk Model I. 

Thus, the final form of Risk Model I is given by... 

The goal of Approach 3 is to append an operational risk term to the mean-risk model formulation in Approach 2 to account for the significance of both financial risk (as considered by Approach 1) and operational risk in decision-making. 

Note that the index s and the corresponding set S is used to denote scenarios for the evaluation of the inner expectation term to distinguish them from the original index s used to represent the scenarios. Vs is weighted by the operational risk factor 02 e (0, oo). The formulation of Risk Model II is ... 

Therefore, in this approach, we develop Risk Model III as a reformulation of Risk Model II by employing the mean-absolute deviation (MAD), in place of variance, as the measure of operational risk imposed by the recourse costs to handle the same three factors of uncertainty (prices, demands, and yields). To the best of our knowledge, this is the first such application of MAD, a widely-used metric in the area of system identification and process control, for risk management in refinery planning. 

Similar to Risk Model II, the adoption of MAD is weighted by the operational risk factor 03 (0 < 03 < oo) in Risk Model III, to give the following formulation ... 

As the main focus of this chapter is on the risk-incorporated models of Risk Models II and III, the computational results for Risk Model I are not presented here. 

As in the case of Risk Model I, the computational results for Expectation Models I and II are not presented here as the emphasis of this chapter is on explaining the concept of risk analysis. 

The formulation of Risk Model 11 for the numerical example is given by the following ... 

Tables 6.3-6.5 show the computational results for Risk Model II over a range of values of risk parameter 02 with respect to different recourse penalty costs, for three representative cases of 0 = 1E — 10, IE — 7, and 1.55E — 5, respectively. An example of the detailed results is presented in Table 6.6 for 02 = 50 of the first case. Figure 6.2 illustrates the corresponding efficient frontier plot for Risk Model II while Figure 6.3 provides the plot of the expected profit for different levels of risk.

Table 6.3 Representative computational results for Risk Model 11 for 0n = 1E — 10. 

Figure 6.2 Risk Model II efficient frontier plot.

Figure 6.3 Risk Model II plot of expected profit for different levels of risk as represented by the economic risk factor 0n and the operational risk factor 02.

From Table 6.7 and the corresponding efficient frontier plot in Figure 6.4, similar trends to Risk Model II (and also the expected value models) are observed in which decreasing values of 0 correspond to higher expected profit until a certain constant profit value is attained ( 81 770). The converse is also true in which a constant profit of 59330 is reached in the initially declining expected profit for increasing values of 0i. 

Figure 6.4 Risk Model III efficient frontier plot.

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