On The Quantitative Definition of Risk

A quantitative definition of risk is suggested in terms of the idea of a "set of triplets". The definition is extended to include uncertainty and completeness, and the use of Bayes' theorem is described in this connection. The definition is used to discuss the notions of "relative risk", "relativity of risk", and "acceptability of risk".     

Multiobjective Decision-Tree Analysis1

Single-objective-based decision-tree analysis has been extensively and successfully used in numerous decision-making problems since its formal introduction by Howard Raiffa more than two decades ago. This paper extends the traditional methodology to incorporate multiple noncommensurate objective functions and use of the conditional expected value of the risk of extreme and catastrophic events. The proposed methodology considers the cases where (a) a finite number of actions are available at each decision node and (b) discrete or continuous states of nature can be presented at each chance node. The proposed extension of decision-tree analysis is introduced through an example problem that leads the reader step-by-step into the methodological procedure. The example problem builds on flood warning systems. Two noncommensurate objectives—the loss of lives and the loss of property (including monetary costs of the flood warning system)–are incorporated into the decision tree. In addition, two risk measures—the common expected value and the conditional expected value of extreme and catastrophic events—are quantified and are also incorporated into the decision-making process. Theoretical difficulties associated with the stage-wise calculation of conditional expected values are identified and certain simplifying assumptions are made for computational tractibility. In particular, it is revealed that decisions concerning experimentation have a very interesting impact on the noninferior solution set of options—a phenomenon that has no equivalence in the single-objective case.     

Artifactual Uncertainty in Risk Analysis

The field of comparative risk analysis of electrical energy alternatives has traditionally been plagued by highly uncertain estimates of risk rates, and consequently by conflicting judgements of relative risk. To the extent that this uncertainty arises from traditional sources–imperfect observations or actual variance in the data–it can be brought within a Bayesian statistical framework which allows policy conclusions to be formulted and tested at different levels of confidence. It is shown that there are important methodological or "artifactual" sources of uncertainty, however, that cannot be treated by statistical means; these require conceptual advances for their resolution. By identifying these sources of uncertainty in simple thought experiments and examples, it is shown in what ways the concept of attributable risk, which is the policy-maker's chief concern, must be sharpened and refined to have unambiguous meaning. The conventional "multilinear" formula for calculating risk indices is challenged as a measure of attributable risk, and directions for further research to improve the methodological foundations of comparative risk analysis are identified.     

Representation,Propagation, and Decision Issues in Risk Analysis Under Incomplete Probabilistic Information

This article tries to clarify the potential role to be played by uncertainty theories such as imprecise probabilities, random sets, and possibility theory in the risk analysis process. Instead of opposing an objective bounding analysis, where only statistically founded probability distributions are taken into account, to the full‐fledged probabilistic approach, exploiting expert subjective judgment, we advocate the idea that both analyses are useful and should be articulated with one another. Moreover, the idea that risk analysis under incomplete information is purely objective is misconceived. The use of uncertainty theories cannot be reduced to a choice between probability distributions and intervals. Indeed, they offer representation tools that are more expressive than each of the latter approaches and can capture expert judgments while being faithful to their limited precision. Consequences of this thesis are examined for uncertainty elicitation, propagation, and at the decision‐making step.     

Intelligent Adversary Risk Analysis: A Bioterrorism Risk Management Model

The tragic events of 9/11 and the concerns about the potential for a terrorist or hostile state attack with weapons of mass destruction have led to an increased emphasis on risk analysis for homeland security. Uncertain hazards (natural and engineering) have been successfully analyzed using probabilistic risk analysis (PRA). Unlike uncertain hazards, terrorists and hostile states are intelligent adversaries who can observe our vulnerabilities and dynamically adapt their plans and actions to achieve their objectives. This article compares uncertain hazard risk analysis with intelligent adversary risk analysis, describes the intelligent adversary risk analysis challenges, and presents a probabilistic defender–attacker–defender model to evaluate the baseline risk and the potential risk reduction provided by defender investments. The model includes defender decisions prior to an attack; attacker decisions during the attack; defender actions after an attack; and the uncertainties of attack implementation, detection, and consequences. The risk management model is demonstrated with an illustrative bioterrorism problem with notional data.     

Historical Application of a Social Amplification of Risk Model: Economic Impacts of Risk Events at Nuclear Weapons Facilities

Public perception of risk is being cited as a documented reason to rethink a very contentious congressionally mandated process for siting interim storage and permanent disposal facilities for high-level radioactive waste. Rigorous survey research has shown that the public holds intense, negative images of "nuclear" and "radioactive" technologies, activities, and facilities. Potential host states and opponents claim that these negative images, coupled with an amplification of negative risk events, will potentially stigmatize the area surrounding such facilities and result in significant economic losses. At issue is whether a supporting social amplification of risk model is applicable to communities hosting facilities that are part of the U.S. Department of Energy Nuclear Weapons Complex. An initial assessment of high-profile discrete and cumulative key negative risk events at such nuclear facilities does not validate that there has been stigmatization or substantial social and economic consequences in the host areas. Before any changes to major national policy are implemented, additional research is required to determine if the nearby public's "pragmatic logic," based on practical knowledge and experience, attenuates the link between public opinion and demographic and economic behaviors.     

Multiobjective Risk-Impact Analysis Method

This paper integrates two methodologies of risk and impact analysis—the partitioned multiobjective risk method (PMRM) and the multiobjective, multistage impact analysis method (MMIAM). The PMRM, in an effort to overcome the difficulties created by commensurating extreme events that have catastrophic impacts with those that have more frequent but less harmful consequences, introduces the use of conditional expectations for different regimes of probabilities and damages. The MMIAM is a multiobjective decisionmaking method for impact analysis which explicitly develops trade-offs among different objectives at different stages or periods. Decision makers who must act under conditions of extreme risk and uncertainty often find that they are more interested in knowing "what not to do" than they are in optimizing their current objectives (the more traditional aim of decision-making methodologies). This paper focuses on a way to answer their needs, in which major elements of both the PMRM and the MMIAM are combined in a new, integrated methodology, termed here the multiobjective risk-impact analysis method (MRIAM). The new methodology incorporates risk and impact analysis within a dynamic multiobjective decision-making framework. To demonstrate the usefulness of the integrated methodology, an example problem concerning the environmental effects of pollutant emissions over a number of years is formulated, solved, and analyzed.     

Risk and Uncertainty Analysis in Government Safety Decisions

Probabilistic risk analysis (PRA) can be an effective tool to assess risks and uncertainties and to set priorities among safety policy options. Based on systems analysis and Bayesian probability, PRA has been applied to a wide range of cases, three of which are briefly presented here: the maintenance of the tiles of the space shuttle, the management of patient risk in anesthesia, and the choice of seismic provisions of building codes for the San Francisco Bay Area. In the quantification of a risk, a number of problems arise in the public sector where multiple stakeholders are involved. In this article, I describe different approaches to the treatments of uncertainties in risk analysis, their implications for risk ranking, and the role of risk analysis results in the context of a safety decision process. I also discuss the implications of adopting conservative hypotheses before proceeding to what is, in essence, a conditional uncertainty analysis, and I explore some implications of different levels of "conservatism" for the ranking of risk mitigation measures.     

Integrated Analysis: Combining Risk and Economic Assessments While Preserving the Separation of Powers

This article presents a process for an integrated policy analysis that combines risk assessment and benefit-cost analysis. This concept, which explicitly combines the two types of related analyses, seems to contradict the long-accepted risk analysis paradigm of separating risk assessment and risk management since benefit-cost analysis is generally considered to be a part of risk management. Yet that separation has become a problem because benefit-cost analysis uses risk assessment results as a starting point and considerable debate over the last several years focused on the incompatibility of the use of upper bounds or "safe" point estimates in many risk assessments with benefit-cost analysis. The problem with these risk assessments is that they ignore probabilistic information. As advanced probabilistic techniques for risk assessment emerge and economic analysts receive distributions of risks instead of point estimates, the artificial separation between risk analysts and the economic/decision analysts complicates the overall analysis. In addition, recent developments in countervailing risk theory suggest that combining the risk and benefit-cost analyses is required to fully understand the complexity of choices and tradeoffs faced by the decisionmaker. This article also argues that the separation of analysis and management is important, but that benefit-cost analysis has been wrongly classified into the risk management category and that the analytical effort associated with understanding the economic impacts of risk reduction actions need to be part of a broader risk assessment process.     

What Defines Us as Professionals in the Field of Risk Analysis?

In a recent issue of Risk Analysis, the then‐President of the Society for Risk Analysis (SRA), Pamela Williams, has some interesting reflections about the risk analysis field. She states that the ability and desire to tackle difficult problems using a risk analytical approach is what uniquely defines us as professionals in the field of risk analysis. The point of departure for her discussion is interviews with the plenary speakers of the 2014 SRA Annual Meeting, who addressed two divisive topics: hydraulic fracking and marijuana use. She points to several themes that invite contributions from the field of risk analysis, including: Has the full spectrum of potential risks and benefits been identified and weighted, and what are the risk tradeoffs or countervailing risks? Inspired by Williams's reflections, and by analyzing the issues raised in the interviews, this article seeks to clarify what our field is really providing. A main conclusion of the article is that it is essential to acknowledge that professionals in the field of risk analysis merely support the tackling of such problems, and that their genuine competence—that which distinguishes them from other professionals—lies in the risk analytical approach itself.     

Combining Probability Distributions From Experts in Risk Analysis

This paper concerns the combination of experts' probability distributions in risk analysis, discussing a variety of combination methods and attempting to highlight the important conceptual and practical issues to be considered in designing a combination process in practice. The role of experts is important because their judgments can provide valuable information, particularly in view of the limited availability of hard data regarding many important uncertainties in risk analysis. Because uncertainties are represented in terms of probability distributions in probabilistic risk analysis (PRA), we consider expert information in terms of probability distributions. The motivation for the use of multiple experts is simply the desire to obtain as much information as possible. Combining experts' probability distributions summarizes the accumulated information for risk analysts and decision-makers. Procedures for combining probability distributions are often compartmentalized as mathematical aggregation methods or behavioral approaches, and we discuss both categories. However, an overall aggregation process could involve both mathematical and behavioral aspects, and no single process is best in all circumstances. An understanding of the pros and cons of different methods and the key issues to consider is valuable in the design of a combination process for a specific PRA. The output, a combined probability distribution, can ideally be viewed as representing a summary of the current state of expert opinion regarding the uncertainty of interest.     

A Social Network Contagion Theory of Risk Perception

Risk perceptions have, to a great extent, been studied exclusively as individual cognitive mechanisms in which individuals collect, process, and form perceptions as atomized units unconnected to a social system. These individual-level theories do not, however, help explain how perception of risk may vary between communities or within a single community. One alternative approach is based on a network theory of contagion. This approach, emerging largely from organizational and community social network studies, suggests that it is the relational aspects of individuals and the resulting networks and self-organizing systems that influence individual perceptions and build "groups or communities of like-minded" individuals. These social units, it is argued, behave as attitude, knowledge, or behavioral structures. The study reported in this article tests one aspect of this theoretical perspective. The central hypothesis proposes the existence of risk perception networks--relational groupings of individuals who share, and perhaps create, similar risk perceptions. To test this idea, data were collected from individuals involved in a community environmental conflict over a hazardous waste site cleanup. The statistical analysis used a matrix of relational social linkages to compare with a matrix of individual risk perceptions The analysis confirmed the hypothesis suggesting that social linkages in communities may play an important role in focusing risk perceptions.     

What Risks Do People Perceive in Everyday Life? A Perspective Gained from the Experience Sampling Method (ESM)

The experience sampling method (ESM) was used to collect data from 74 part-time students who described and assessed the risks involved in their current activities when interrupted at random moments by text messages. The major categories of perceived risk were short term in nature and involved "loss of time or materials" related to work and "physical damage" (e.g., from transportation). Using techniques of multilevel analysis, we demonstrate effects of gender, emotional state, and types of risk on assessments of risk. Specifically, females do not differ from males in assessing the potential severity of risks but they see these as more likely to occur. Also, participants assessed risks to be lower when in more positive self-reported emotional states. We further demonstrate the potential of ESM by showing that risk assessments associated with current actions exceed those made retrospectively. We conclude by noting advantages and disadvantages of ESM for collecting data about risk perceptions.     

On Some Recent Definitions and Analysis Frameworks for Risk,Vulnerability, and Resilience

Recently, considerable attention has been paid to a systems‐based approach to risk, vulnerability, and resilience analysis. It is argued that risk, vulnerability, and resilience are inherently and fundamentally functions of the states of the system and its environment. Vulnerability is defined as the manifestation of the inherent states of the system that can be subjected to a natural hazard or be exploited to adversely affect that system, whereas resilience is defined as the ability of the system to withstand a major disruption within acceptable degradation parameters and to recover within an acceptable time, and composite costs, and risks. Risk, on the other hand, is probability based, defined by the probability and severity of adverse effects (i.e., the consequences). In this article, we look more closely into this approach. It is observed that the key concepts are inconsistent in the sense that the uncertainty (probability) dimension is included for the risk definition but not for vulnerability and resilience. In the article, we question the rationale for this inconsistency. The suggested approach is compared with an alternative framework that provides a logically defined structure for risk, vulnerability, and resilience, where all three concepts are incorporating the uncertainty (probability) dimension.     

Probabilistic Risk Analysis for a High-Level Radioactive Waste Repository

A probabilistic risk analysis (PRA) for a high-level radioactive waste repository is very important since it gives an estimate of its health impacts, allowing comparisons to be made with the health impacts of competing technologies. However, it is extremely difficult to develop a credible PRA for a specific repository site because of large uncertainties in future climate, hydrology, geological processes, etc. At best, such a PRA would not be understandable to the public. An alternative proposed here is to develop a PRA for an average U.S. site, taking all properties of the site to be the U.S. average. The results are equivalent to the average results for numerous randomly selected sites. Such a PRA is presented here; it is easy to understand, and it is not susceptible to substantial uncertainty. Applying the results to a specific repository site then requires only a simple, intuitively acceptable "leap of faith" in assuming that with large expenditures of effort and money, experts can select a site that would be at least as secure as a randomly selected site.     

Farmer Knowledge and Risk Analysis: Postrelease Evaluation of Herbicide-Tolerant Canola in Western Canada

The global controversy regarding the use of genetically modified (GM) crops has proved to be a challenge for "science-based" risk assessments. Although risk analysis incorporates societal perspectives in decision making over these crops, it is largely predicated on contrasts between "expert" and "lay" perspectives. The overall objective of this study is to explore the role for farmers' knowledge, and their decade-long experience with herbicide-tolerant (HT) canola, in the risk analysis of GM crops. From 2002 to 2003, data were collected using interviews ( n = 15) and mail surveys ( n = 370) with farmers from Manitoba and across Canada. The main benefits associated with HT canola were management oriented and included easier weed control, herbicide rotation, and better weed control, whereas the main risks were more diverse and included market harm, technology use agreements (TUAs), and increased seed costs. Benefits and risks were inversely related, and the salient factor influencing risk was farmer experiences with HT canola volunteers, followed by small farm size and duration using HT canola. These HT volunteers were reported by 38% of farmers, from both internal (e.g., seedbank, farm machinery, etc.) and external (e.g., wind, seed contamination, etc.) sources, and were found to persist over time. Farmer knowledge is a reliable and rich source of information regarding the efficacy of HT crops, demonstrating that individual experiences are important to risk perception. The socioeconomic nature of most risks combined with the continuing "farm income crisis" in North America demonstrates the need for a more holistic and inclusive approach to risk assessment associated with HT crops and, indeed, with all new agricultural technology.     

LP/HC and LULUs: The Political Uses of Risk Analysis in Land-Use Planning1

This paper examines how LP/HC (low-probability/high-consequence) risk analysis is used in planning for locally unwanted land uses, or LULUs. LULUs are development projects that are predictably objectionable to many of their neighbors. Examples are nuclear power plants, hazardous waste facilities, refineries, and airports. The paper begins by elaborating the idea of LULUs, focussing on those whose planning typically requires or invokes some form of LP/HC risk analysis. It then discusses how land planning and planners actually use the LP/HC approach to deal with LULUs. It argues that in practice land-use planners and their associates employ a concept of risk different from that of economists, scientists, and engineers and more like that of political decision-makers and the public at large. It concludes with a political interpretation that offers some suggestions for productively reducing this divergence in the treatment of LULUs that pose LP/HC risks.     

Mental Models in Risk Assessment: Informing People About Drugs

One way to communicate about the risks of drugs is through the use of package inserts. The problems associated with this medium of informing patients have been investigated by several researchers who found that people require information about drugs they are using, including extensive risk information, and that they are willing to take this information into account in their usage of drugs. But empirical results also show that people easily misinterpret the information given. A conceptual framework is proposed that might be used for better understanding the cognitive processes involved in such a type of risk assessment and communication. It is based on the idea that people develop, through experience, a mental model of how a drug works, which effects it might produce, that contraindications have to be considered, etc. This mental model is "run" when a specific package insert has been read and a specific question arises such as, for example, whether certain symptoms can be explained as normal or whether they require special attention and action. We argue that the mental model approach offers a useful perspective for examining how people understand package inserts, and consequently for improving their content and design. The approach promises to be equally useful for other aspects of risk analysis that are dependent upon human judgment and decision making, e.g., threat diagnosis and human reliability analysis.     

基于实物期权的企业兼并行为分析

利用实物期权博弈论等理论和方法,研究信息完全条件下有负债企业兼并的均衡价格和最优时机.通过对随机市场下企业兼并的动机、过程的微观机理的深入剖析,对影响兼并定价的主要因素进行分析,分别给出随机市场下有负债的"好企业"增资扩股的均衡条件和最优时机的解析式,以及对"一般企业"和"差企业"兼并的最优时机和均衡价格的解析式,并进行比较静态分析和数值模拟.研究结论与经验相符.