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 of Extreme Events in Multiobjective Decision Trees Part 1. Severe Events

Earlier work with decision trees identified nonseparability as an obstacle to minimizing the conditional expected value, a measure of the risk of extreme events, by the well-known method of averaging out and folding back. This first of two companion papers addresses the conditional expected value that is defined as the expected outcome assuming the exceedance of a threshold β, where β is preselected by the decision maker. An approach is proposed to overcome the need to evaluate all policies in order to identify the optimal policy. The approach is based on the insight that the conditional expected value is separable into two constituent elements of risk and can thus be optimized along with other objectives, including the unconditional expected value of the outcome, by using a multiobjective decision tree. An example of sequential decision making for improving highway capacity is given.     

Risk of Extreme Events in Multiobjective Decision Trees Part 2. Rare Events

Earlier work with decision trees identified nonseparability as an obstacle to minimizing the conditional expected value, a measure of the risk of extreme events, by the well-known method of averaging out and folding back. This second of two companion papers addresses the conditional expected value that is defined as the expected outcome assuming that a random variable is observed only in the upper 100 (1 −α) percent of potential outcomes, where α is a cumulative probability preselected by the decision maker. An approach is proposed to overcome the need to evaluate all policies in order to identify the optimal policy. The approach is based in part on approximating the conditional expected value by using statistics of extremes. An existing convenient approximation of the conditional expected value is shown to be separable into two constituent elements of risk and can thus be optimized, along with other objectives including the unconditional expected value of the outcome, in a multiobjective decision tree. An example of sequential decision making for remediation or environmental contamination is provided. The importance of the results for risk analyis beyond the minimization of conditional expected values is pointed out.     

Selection of Probability Distributions in Characterizing Risk of Extreme Events

Use of probability distributions by regulatory agencies often focuses on the extreme events and scenarios that correspond to the tail of probability distributions. This paper makes the case that assessment of the tail of the distribution can and often should be performed separately from assessment of the central values. Factors to consider when developing distributions that account for tail behavior include (a) the availability of data, (b) characteristics of the tail of the distribution, and (c) the value of additional information in assessment. The integration of these elements will improve the modeling of extreme events by the tail of distributions, thereby providing policy makers with critical information on the risk of extreme events. Two examples provide insight into the theme of the paper. The first demonstrates the need for a parallel analysis that separates the extreme events from the central values. The second shows a link between the selection of the tail distribution and a decision criterion. In addition, the phenomenon of breaking records in time-series data gives insight to the information that characterizes extreme values. One methodology for treating risk of extreme events explicitly adopts the conditional expected value as a measure of risk. Theoretical results concerning this measure are given to clarify some of the concepts of the risk of extreme events.     

A Probabilistic Model of the Economic Risk to Britain's Railway Network from Bridge Scour During Floods

Scour (localized erosion by water) is an important risk to bridges, and hence many infrastructure networks, around the world. In Britain, scour has caused the failure of railway bridges crossing rivers in more than 50 flood events. These events have been investigated in detail, providing a data set with which we develop and test a model to quantify scour risk. The risk analysis is formulated in terms of a generic, transferrable infrastructure network risk model. For some bridge failures, the severity of the causative flood was recorded or can be reconstructed. These data are combined with the background failure rate, and records of bridges that have not failed, to construct fragility curves that quantify the failure probability conditional on the severity of a flood event. The fragility curves generated are to some extent sensitive to the way in which these data are incorporated into the statistical analysis. The new fragility analysis is tested using flood events simulated from a spatial joint probability model for extreme river flows for all river gauging sites in Britain. The combined models appear robust in comparison with historical observations of the expected number of bridge failures in a flood event. The analysis is used to estimate the probability of single or multiple bridge failures in Britain's rail network. Combined with a model for passenger journey disruption in the event of bridge failure, we calculate a system‐wide estimate for the risk of scour failures in terms of passenger journey disruptions and associated economic costs.     

Adjexpectile风险测度的性质、优化及资产配置的应用

金融风险的度量和识别是风险管理的重要内容,常用的风险度量工具是标准差、VaR、ES,但存在很多缺陷,expectile的提出弥补了这些不足,在理论界得到广泛的讨论和应用。本文扩展了expectile进行资产配置,提出Adjexpectile的概念,并讨论和分析了Adjexpectile的一致性风险度量、随机占优性、凸性,与标准差、VaR、shortfall的关系,风险贡献及风险分解的性质。通过对六个资产指数：上证国债指数、上证企业债指数、上证180指数、深圳100指数、深成长40p指数和黄金现货指数的复合周收益率数据进行组合优化配置,发现Adjexpectile在非对称性收益数据、组合前沿、风险分散方面具有一定的优越性。     

Flash Flood Risks and Warning Decisions: A Mental Models Study of Forecasters,Public Officials,and Media Broadcasters in Boulder,Colorado

Timely warning communication and decision making are critical for reducing harm from flash flooding. To help understand and improve extreme weather risk communication and management, this study uses a mental models research approach to investigate the flash flood warning system and its risk decision context. Data were collected in the Boulder, Colorado area from mental models interviews with forecasters, public officials, and media broadcasters, who each make important interacting decisions in the warning system, and from a group modeling session with forecasters. Analysis of the data informed development of a decision‐focused model of the flash flood warning system that integrates the professionals’ perspectives. Comparative analysis of individual and group data with this model characterizes how these professionals conceptualize flash flood risks and associated uncertainty; create and disseminate flash flood warning information; and perceive how warning information is (and should be) used in their own and others’ decisions. The analysis indicates that warning system functioning would benefit from professionals developing a clearer, shared understanding of flash flood risks and the warning system, across their areas of expertise and job roles. Given the challenges in risk communication and decision making for complex, rapidly evolving hazards such as flash floods, another priority is development of improved warning content to help members of the public protect themselves when needed. Also important is professional communication with members of the public about allocation of responsibilities for managing flash flood risks, as well as improved system‐wide management of uncertainty in decisions.     

Risk of Extreme Events Under Nonstationary Conditions

The concept of the return period is widely used in the analysis of the risk of extreme events and in engineering design. For example, a levee can be designed to protect against the 100-year flood, the flood which on average occurs once in 100 years. Use of the return period typically assumes that the probability of occurrence of an extreme event in the current or any future year is the same. However, there is evidence that potential climate change may affect the probabilities of some extreme events such as floods and droughts. In turn, this would affect the level of protection provided by the current infrastructure. For an engineering project, the risk of an extreme event in a future year could greatly exceed the average annual risk over the design life of the project. An equivalent definition of the return period under stationary conditions is the expected waiting time before failure. This paper examines how this definition can be adapted to nonstationary conditions. Designers of flood control projects should be aware that alternative definitions of the return period imply different risk under nonstationary conditions. The statistics of extremes and extreme value distributions are useful to examine extreme event risk. This paper uses a Gumbel Type I distribution to model the probability of failure under nonstationary conditions. The probability of an extreme event under nonstationary conditions depends on the rate of change of the parameters of the underlying distribution.     

Community Resilience and Decision Theory Challenges for Catastrophic Events

Extreme and catastrophic events pose challenges for normative models of risk management decision making. They invite development of new methods and principles to complement existing normative decision and risk analysis. Because such events are rare, it is difficult to learn about them from experience. They can prompt both too little concern before the fact, and too much after. Emotionally charged and vivid outcomes promote probability neglect and distort risk perceptions. Aversion to acting on uncertain probabilities saps precautionary action; moral hazard distorts incentives to take care; imperfect learning and social adaptation (e.g., herd‐following, group‐think) complicate forecasting and coordination of individual behaviors and undermine prediction, preparation, and insurance of catastrophic events. Such difficulties raise substantial challenges for normative decision theories prescribing how catastrophe risks should be managed. This article summarizes challenges for catastrophic hazards with uncertain or unpredictable frequencies and severities, hard‐to‐envision and incompletely described decision alternatives and consequences, and individual responses that influence each other. Conceptual models and examples clarify where and why new methods are needed to complement traditional normative decision theories for individuals and groups. For example, prospective and retrospective preferences for risk management alternatives may conflict; procedures for combining individual beliefs or preferences can produce collective decisions that no one favors; and individual choices or behaviors in preparing for possible disasters may have no equilibrium. Recent ideas for building “disaster‐resilient” communities can complement traditional normative decision theories, helping to meet the practical need for better ways to manage risks of extreme and catastrophic events.     

“Know What to Do If You Encounter a Flash Flood”: Mental Models Analysis for Improving Flash Flood Risk Communication and Public Decision Making

Understanding how people view flash flood risks can help improve risk communication, ultimately improving outcomes. This article analyzes data from 26 mental models interviews about flash floods with members of the public in Boulder, Colorado, to understand their perspectives on flash flood risks and mitigation. The analysis includes a comparison between public and professional perspectives by referencing a companion mental models study of Boulder‐area professionals. A mental models approach can help to diagnose what people already know about flash flood risks and responses, as well as any critical gaps in their knowledge that might be addressed through improved risk communication. A few public interviewees mentioned most of the key concepts discussed by professionals as important for flash flood warning decision making. However, most interviewees exhibited some incomplete understandings and misconceptions about aspects of flash flood development and exposure, effects, or mitigation that may lead to ineffective warning decisions when a flash flood threatens. These include important misunderstandings about the rapid evolution of flash floods, the speed of water in flash floods, the locations and times that pose the greatest flash flood risk in Boulder, the value of situational awareness and environmental cues, and the most appropriate responses when a flash flood threatens. The findings point to recommendations for ways to improve risk communication, over the long term and when an event threatens, to help people quickly recognize and understand threats, obtain needed information, and make informed decisions in complex, rapidly evolving extreme weather events such as flash floods.     

Risk Modeling, Assessment, and Management of Lahar Flow Threat

The 1991 eruption of Mount Pinatubo in the Philippines is considered one of the most violent and destructive volcanic activities in the 20th century. Lahar is the Indonesian term for volcanic ash, and lahar flows resulting from the massive amount of volcanic materials deposited on the mountain's slope posed continued post-eruption threats to the surrounding areas, destroying lives, homes, agricultural products, and infrastructures. Risks of lahar flows were identified immediately after the eruption, with scientific data provided by the Philippine Institute of Volcanology, the U.S. Geological Survey, and other research institutions. However, competing political, economic, and social agendas subordinated the importance of scientific information to policy making. Using systemic risk analysis and management, this article addresses the issues of multiple objectives and the effective integration of scientific techniques into the decision-making process. It provides a modeling framework for identifying, prioritizing, and evaluating policies for managing risk. The major considerations are: (1) applying a holistic approach to risk analysis through hierarchical holographic modeling, (2) applying statistical methods to gain insight into the problem of uncertainty in risk assessment, (3) using multiobjective trade-off analysis to address the issue of multiple decisionmakers and stakeholders in the decision-making process, (4) using the conditional expected value of extreme events to complement and supplement the expected value in quantifying risk, and (5) assessing the impacts of multistage decisions. Numerical examples based on ex post data are formulated to illustrate applications to various problems. The resulting framework from this study can serve as a general baseline model for assessing and managing risks of natural disasters, which the Philippines' lead agency-the National Disaster Coordinating Council (NDCC)-and other related organizations can use for their decision-making processes.     

双随机复合泊松损失下巨灾债券定价与数值模拟

上世纪90年代出现的巨灾债券是以规避巨灾财产损失为目的的新型非传统风险转移金融创新工具之一,在我国有良好的发展前景。本文针对巨灾风险事件呈现出周期性与不规则的上升特征,构建了BDT过程用以刻画巨灾风险的抵达过程,并基于风险中性测度技术,在随机利率环境与双随机复合泊松损失条件下,导出了巨灾债券定价公式。进而结合伦敦同业银行拆借利率数据与美国保险服务所提供的PCS损失指数估计并校正了模型参数。最后,通过数值模拟检验了利率风险与巨灾风险如何影响巨灾债券的价格,同时验证了定价模型的可行性。     

基于EVT-POT-SV-MT模型的极值风险度量

针对金融资产收益的异常变化,采用SV-MT模型对风险资产的预期收益做风险补偿并捕捉收益序列的厚尾性、波动的异方差性等特征,将收益序列转化为标准残差序列,通过SV-MT模型与极值理论相结合拟合标准残差的尾部分布,建立了一种新的金融风险度量模型——基于EVT-POT-SV-MT的动态VaR模型.通过该模型对上证综指做实证分析,结果表明该模型能够合理有效地度量上证综指收益的风险.     

A Probabilistic Framework for Risk Analysis of Widespread Flood Events: A Proof‐of‐Concept Study

This article presents a flood risk analysis model that considers the spatially heterogeneous nature of flood events. The basic concept of this approach is to generate a large sample of flood events that can be regarded as temporal extrapolation of flood events. These are combined with cumulative flood impact indicators, such as building damages, to finally derive time series of damages for risk estimation. Therefore, a multivariate modeling procedure that is able to take into account the spatial characteristics of flooding, the regionalization method top‐kriging, and three different impact indicators are combined in a model chain. Eventually, the expected annual flood impact (e.g., expected annual damages) and the flood impact associated with a low probability of occurrence are determined for a study area. The risk model has the potential to augment the understanding of flood risk in a region and thereby contribute to enhanced risk management of, for example, risk analysts and policymakers or insurance companies. The modeling framework was successfully applied in a proof‐of‐concept exercise in Vorarlberg (Austria). The results of the case study show that risk analysis has to be based on spatially heterogeneous flood events in order to estimate flood risk adequately.     

Generalized Quantification of Risk Associated with Extreme Events1

In the partitioned multiobjective risk method (PMRM) the probability axis is typically partitioned into three regimes: high-exceedance low-consequence, intermediate-exceedance intermediate-consequence, and low-exceedance high-consequence (LE/HC). For each regime, the PMRM generates a conditional expected risk-function given that the damage lies within the regime. The theme of this paper is the conditional expected-risk function for the LE/HC regime. This function, denoted by f₄(.), captures the behavior of the “extreme events” of an underlying decision-making problem. The PMRM offers two advantages: (a) it isolates LE/HC events, allowing the decision-maker(s) to focus on the impacts of catastrophies; and (b) it generates more valuable information than that obtained from the common unconditional expected-risk function. Theoretical problems may arise from uncertainty about the behavior of the tail of the risk curve describing the underlying frequency of damages. When the number of physical observations in small (e.g., in flood frequency analysis), the analyst is forced to make assumptions about the density of damages. Each succeeding distributional assumption will generate a different value of f₄(.). An added dimension of difficulty is also created by the sensitivity of f₄(.) to the choice of the boundary of the LE/HC regime. This paper has two overall objectives: (a) to present distribution-free results concerning the magnitude of f₄(.); and (b) to use those results to obtain a distribution-free estimate of the sensitivity of f₄(.) to the choice of the boundary of the LE/HC regime. The above objectives are realized by extending, and further developing, existing inequalities for continuously distributed random variables.     

Risk-Adjusted Mission Value: Trading Off Mission Risk for Mission Value

This article develops a decision-theoretic methodology for the risk-adjusted mission value (RAMV) for selecting between alternative missions in the presence of uncertainty in the outcomes of the missions. This methodology permits trading off mission risk for mission value, something that probabilistic risk analysis cannot do unless it explicitly incorporates both mission value and risk aversion of the project management. The methodology, in its complete implementation, is consistent with the decision theory known as expected utility theory, although it differs from conventional decision theory in that the probabilities and all but one of the utilities are not those of the decision maker. The article also introduces a new interpretation of risk aversion. The methodology is consistent with the elementary management concept concerning division of labor. An example is presented for selecting between discrete alternatives-four landing sites on Mars. A second example is presented for selecting among a set of continuous alternatives-a comet flyby distance. The methodology is developed within the context of scientific missions, but the methodology is equally applicable to any situation requiring outcome value judgments, probability judgments, and risk aversion judgments by different constituencies.     

Structured Coupling of Probability Loss Distributions: Assessing Joint Flood Risk in Multiple River Basins

Losses due to natural hazard events can be extraordinarily high and difficult to cope with. Therefore, there is considerable interest to estimate the potential impact of current and future extreme events at all scales in as much detail as possible. As hazards typically spread over wider areas, risk assessment must take into account interrelations between regions. Neglecting such interdependencies can lead to a severe underestimation of potential losses, especially for extreme events. This underestimation of extreme risk can lead to the failure of riskmanagement strategies when they are most needed, namely, in times of unprecedented events. In this article, we suggest a methodology to incorporate such interdependencies in risk via the use of copulas. We demonstrate that by coupling losses, dependencies can be incorporated in risk analysis, avoiding the underestimation of risk. Based on maximum discharge data of river basins and stream networks, we present and discuss different ways to couple loss distributions of basins while explicitly incorporating tail dependencies. We distinguish between coupling methods that require river structure data for the analysis and those that do not. For the later approach we propose a minimax algorithm to choose coupled basin pairs so that the underestimation of risk is avoided and the use of river structure data is not needed. The proposed methodology is especially useful for large‐scale analysis and we motivate and apply our method using the case of Romania. The approach can be easily extended to other countries and natural hazards.     

Distribution Analyzer and Risk Evaluator (DARE) Using Fault Trees

Risk and uncertainty are integral parts of modern technology, and they must be managed effectively to allow the development of reliable, high-quality products. Because so many facets of technology and society involve risk and uncertainty, it is essential that risk management be handled in a systematic manner. Fault-tree analysis is one of the principal methods used in the analysis of systems'safety. Its detailed and systematic deductive structure makes it a valuable tool for design and diagnostic purposes. Point probability and the minimization of the expected failure probability have, until recently, dominated fault-tree analysis. A methodology that incorporates uncertainty analysis, conditional expected risk, and multiple objectives with fault-tree analysis is presented. A computer software package termed the "Distribution Analyzer and Risk Evaluator (DARE) Using Fault Trees," which translates the new methodology into a working decision-support system, is developed. DARE Using Fault Trees is a flexible computer code that is capable of analyzing the risk of the overall system in terms of the probability density function of failure probability. Emphasis is placed on the uncertainty and risk of extreme events. A comparative study between existing codes for fault-tree analysis and DARE demonstrates the strengths of the methodology. A case study for NASA's solid rocket booster is used to perform the comparative analysis.     

The Effects of Revealed Information on Catastrophe Loss Projection Models’ Characterization of Risk: Damage Vulnerability Evidence from Florida

We examine whether the risk characterization estimated by catastrophic loss projection models is sensitive to the revelation of new information regarding risk type. We use commercial loss projection models from two widely employed modeling firms to estimate the expected hurricane losses of Florida Atlantic University's building stock, both including and excluding secondary information regarding hurricane mitigation features that influence damage vulnerability. We then compare the results of the models without and with this revealed information and find that the revelation of additional, secondary information influences modeled losses for the windstorm‐exposed university building stock, primarily evidenced by meaningful percent differences in the loss exceedance output indicated after secondary modifiers are incorporated in the analysis. Secondary risk characteristics for the data set studied appear to have substantially greater impact on probable maximum loss estimates than on average annual loss estimates. While it may be intuitively expected for catastrophe models to indicate that secondary risk characteristics hold value for reducing modeled losses, the finding that the primary value of secondary risk characteristics is in reduction of losses in the “tail” (low probability, high severity) events is less intuitive, and therefore especially interesting. Further, we address the benefit‐cost tradeoffs that commercial entities must consider when deciding whether to undergo the data collection necessary to include secondary information in modeling. Although we assert the long‐term benefit‐cost tradeoff is positive for virtually every entity, we acknowledge short‐term disincentives to such an effort.     

基于CVaR约束的多产品订货风险决策模型

过去随机环境下多产品订货往往以期望值作为唯一决策准则,没有将风险控制纳入决策范畴,与实际决策过程不相符合.为给具有不同风险偏好的决策者提供合适的决策分析工具,文章在分析投资组合和产品组合存在某种相似性的基础上,借鉴金融工程领域广泛应用的条件风险值方法,建立多产品最优订货决策模型,并对模型进行了检验,发现它完全符合决策者的直觉要求.而且,由于所建的模型最终可以表示为一个线性规划问题,因此即使是大规模的产品组合问题也可以借助工具软件求解.