The Use of Simulation to Reduce the Domain of “Black Swans” with Application to Hurricane Impacts to Power Systems

Recently, the concept of black swans has gained increased attention in the fields of risk assessment and risk management. Different types of black swans have been suggested, distinguishing between unknown unknowns (nothing in the past can convincingly point to its occurrence), unknown knowns (known to some, but not to relevant analysts), or known knowns where the probability of occurrence is judged as negligible. Traditional risk assessments have been questioned, as their standard probabilistic methods may not be capable of predicting or even identifying these rare and extreme events, thus creating a source of possible black swans. In this article, we show how a simulation model can be used to identify previously unknown potentially extreme events that if not identified and treated could occur as black swans. We show that by manipulating a verified and validated model used to predict the impacts of hazards on a system of interest, we can identify hazard conditions not previously experienced that could lead to impacts much larger than any previous level of impact. This makes these potential black swan events known and allows risk managers to more fully consider them. We demonstrate this method using a model developed to evaluate the effect of hurricanes on energy systems in the United States; we identify hurricanes with potentially extreme impacts, storms well beyond what the historic record suggests is possible in terms of impacts.     

Setting Risk Priorities: A Formal Model

This article presents a model designed to capture the major aspects of setting priorities among risks, a common task in government and industry. The model has both design features, under the control of the rankers (e.g., how success is evaluated), and context features, properties of the situations that they are trying to understand (e.g., how quickly uncertainty can be reduced). The model is demonstrated in terms of two extreme ranking strategies. The first, sequential risk ranking , devotes all its resources, in a given period, to learning more about a single risk, and its place in the overall ranking. This strategy characterizes the process for a society (or organization or individual) that throws itself completely into dealing with one risk after another. The other extreme strategy, simultaneous risk ranking , spreads available resources equally across all risks. It characterizes the most methodical of ranking exercises. Given ample ranking resources, simultaneous risk ranking will eventually provide an accurate set of priorities, whereas sequential ranking might never get to some risks. Resource constraints, however, may prevent simultaneous rankers from examining any risk very thoroughly. The model is intended to clarify the nature of ranking tasks, predict the efficacy of alternative strategies, and improve their design.     

System of Systems Engineering and Risk Management of Extreme Events: Concepts and Case Study

The domain of risk analysis is expanded to consider strategic interactions among multiple participants in the management of extreme risk in a system of systems. These risks are fraught with complexity, ambiguity, and uncertainty, which pose challenges in how participants perceive, understand, and manage risk of extreme events. In the case of extreme events affecting a system of systems, cause‐and‐effect relationships among initiating events and losses may be difficult to ascertain due to interactions of multiple systems and participants (complexity). Moreover, selection of threats, hazards, and consequences on which to focus may be unclear or contentious to participants within multiple interacting systems (ambiguity). Finally, all types of risk, by definition, involve potential losses due to uncertain events (uncertainty). Therefore, risk analysis of extreme events affecting a system of systems should address complex, ambiguous, and uncertain aspects of extreme risk. To accomplish this, a system of systems engineering methodology for risk analysis is proposed as a general approach to address extreme risk in a system of systems. Our contribution is an integrative and adaptive systems methodology to analyze risk such that strategic interactions among multiple participants are considered. A practical application of the system of systems engineering methodology is demonstrated in part by a case study of a maritime infrastructure system of systems interface, namely, the Straits of Malacca and Singapore.     

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.     

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.     

Spatial Risk Analysis of Power Systems Resilience During Extreme Events

The increased frequency of extreme events in recent years highlights the emerging need for the development of methods that could contribute to the mitigation of the impact of such events on critical infrastructures, as well as boost their resilience against them. This article proposes an online spatial risk analysis capable of providing an indication of the evolving risk of power systems regions subject to extreme events. A Severity Risk Index (SRI) with the support of real‐time monitoring assesses the impact of the extreme events on the power system resilience, with application to the effect of windstorms on transmission networks. The index considers the spatial and temporal evolution of the extreme event, system operating conditions, and the degraded system performance during the event. SRI is based on probabilistic risk by condensing the probability and impact of possible failure scenarios while the event is spatially moving across a power system. Due to the large number of possible failures during an extreme event, a scenario generation and reduction algorithm is applied in order to reduce the computation time. SRI provides the operator with a probabilistic assessment that could lead to effective resilience‐based decisions for risk mitigation. The IEEE 24‐bus Reliability Test System has been used to demonstrate the effectiveness of the proposed online risk analysis, which was embedded in a sequential Monte Carlo simulation for capturing the spatiotemporal effects of extreme events and evaluating the effectiveness of the proposed method.     

Vulnerability and Risk: Some Thoughts from a Political and Policy Perspective

Public policies to mitigate the impacts of extreme events such as hurricanes or terrorist attacks will differ depending on whether they focus on reducing risk or reducing vulnerability. Here we present and defend six assertions aimed at exploring the benefits of vulnerability-based policies. (1) Risk-based approaches to covering the costs of extreme events do not depend for their success on reduction of vulnerability. (2) Risk-based approaches to preparing for extreme events are focused on acquiring accurate probabilistic information about the events themselves. (3) Understanding and reducing vulnerability does not demand accurate predictions of the incidence of extreme events. (4) Extreme events are created by context. (5) It is politically difficult to justify vulnerability reduction on economic grounds. (6) Vulnerability reduction is a human rights issue; risk reduction is not.     

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.     

Extreme Risk Analysis of Interdependent Economic and Infrastructure Sectors

Willful attacks or natural disasters pose extreme risks to sectors of the economy. An extreme-event analysis extension is proposed for the Inoperability Input-Output Model (IIM) and the Dynamic IIM (DIIM), which are analytical methodologies for assessing the propagated consequences of initial disruptions to a set of sectors. The article discusses two major risk categories that the economy typically experiences following extreme events: (i) significant changes in consumption patterns due to lingering public fear and (ii) adjustments to the production outputs of the interdependent economic sectors that are necessary to match prevailing consumption levels during the recovery period. Probability distributions associated with changes in the consumption of directly affected sectors are generated based on trends, forecasts, and expert evidence to assess the expected losses of the economy. Analytical formulations are derived to quantify the extreme risks associated with a set of initially affected sectors. In addition, Monte Carlo simulation is used to handle the more complex calculations required for a larger set of sectors and general types of probability distributions. A two-sector example is provided at the end of the article to illustrate the proposed extreme risk model formulations.     

A Framework to Understand Extreme Space Weather Event Probability

An extreme space weather event has the potential to disrupt or damage infrastructure systems and technologies that many societies rely on for economic and social well‐being. Space weather events occur regularly, but extreme events are less frequent, with a small number of historical examples over the last 160 years. During the past decade, published works have (1) examined the physical characteristics of the extreme historical events and (2) discussed the probability or return rate of select extreme geomagnetic disturbances, including the 1859 Carrington event. Here we present initial findings on a unified framework approach to visualize space weather event probability, using a Bayesian model average, in the context of historical extreme events. We present disturbance storm time (Dst ) probability (a proxy for geomagnetic disturbance intensity) across multiple return periods and discuss parameters of interest to policymakers and planners in the context of past extreme space weather events. We discuss the current state of these analyses, their utility to policymakers and planners, the current limitations when compared to other hazards, and several gaps that need to be filled to enhance space weather risk assessments.     

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.     

Physician anger--Part 1. Changing perception: an interview with Charles E. Dwyer, PhD. Interview by Richard L. Reece.

On January 21, Richard Reece, MD, interviewed Charles E. Dwyer, PhD, to talk about solutions for changing the perceptions of today's beleaguered physicians. He discusses the state of affairs of physician executives in this turbulent industry and how they need to move beyond their thinking about organizations and their current responses to change. The key, Dwyer emphasizes, is influencing people to do what you want them to do. "If you want somebody to do something other than what they are doing now, then you must bring them to perceive that what you want them to do is better than what they are doing now in terms of what is important to them." He also explores how physicians can change their responses to the health care environment: "You can actually decide how you are going to respond conceptually, emotionally, and behaviorally to anything that happens in your life." Part 2 of this interview will appear in the upcoming May/June issue and will provide hands-on strategies for dealing with physician anger, fear, and resentment.     

极端情况下对我国股市风险的实证研究

准确地度量风险是对风险进行有效管理的前提也是投资者做出合理的投资决策的基础,然而在极端事件频繁发生的情况下,传统的VaR计算方法难以准确地度量股市风险,极值理论却可以很好地解决这一问题。本文特别关注了由2007年美国"次贷" 危机所引发的全球金融危机爆发时我国股市的风险度量问题,考虑到全球股市间极端事件的联动效应,利用基于极值理论的POT模型对上证综指日收益率的尾部数据直接建模拟合分布,进而计算出风险值VaR和CVaR,通过比较危机前后的风险值,发现随着金融危机的到来,我国股市的风险有了一定程度的释放。     

Projections of Future Extreme Weather Losses Under Changes in Climate and Exposure

Many attempts are made to assess future changes in extreme weather events due to anthropogenic climate change, but few studies have estimated the potential change in economic losses from such events. Projecting losses is more complex as it requires insight into the change in the weather hazard but also into exposure and vulnerability of assets. This article discusses the issues involved as well as a framework for projecting future losses, and provides an overview of some state‐of‐the‐art projections. Estimates of changes in losses from cyclones and floods are given, and particular attention is paid to the different approaches and assumptions. All projections show increases in extreme weather losses due to climate change. Flood losses are generally projected to increase more rapidly than losses from tropical and extra‐tropical cyclones. However, for the period until the year 2040, the contribution from increasing exposure and value of capital at risk to future losses is likely to be equal or larger than the contribution from anthropogenic climate change. Given the fact that the occurrence of loss events also varies over time due to natural climate variability, the signal from anthropogenic climate change is likely to be lost among the other causes for changes in risk, at least during the period until 2040. More efforts are needed to arrive at a comprehensive approach that includes quantification of changes in hazard, exposure, and vulnerability, as well as adaptation effects.     

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。     

“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.     

A Survey of Approaches for Assessing and Managing the Risk of Extremes

In this paper, we review methods for assessing and managing the risk of extreme events, where extreme events are defined to be rare, severe, and outside the normal range of experience of the system in question. First, we discuss several systematic approaches for identifying possible extreme events. We then discuss some issues related to risk assessment of extreme events, including what type of output is needed (e.g., a single probability vs. a probability distribution), and alternatives to the probabilistic approach. Next, we present a number of probabilistic methods. These include: guidelines for eliciting informative probability distributions from experts; maximum entropy distributions; extreme value theory; other approaches for constructing prior distributions (such as reference or noninformative priors); the use of modeling and decomposition to estimate the probability (or distribution) of interest; and bounding methods. Finally, we briefly discuss several approaches for managing the risk of extreme events, and conclude with recommendations and directions for future research.     

考虑投资者情绪的中国股市自激发效应研究

本文在极值理论中引入行为金融学，结合标值自激发点过程（MSEPP）刻画股指收益率极端值序列的集聚性、短期相依性，并将传统的超阈值模型所描述的齐次泊松过程拓展为非齐次泊松过程，探讨投资者情绪对极端收益率的冲击。运用风险偏好指数的方法，基于沪深300指数成份股合成中国投资者情绪指数（EMSI），进一步构建MSEPP-EMSI模型预测沪深300指数、上证综合指数及深圳成分指数的极端风险爆发概率，并对其进行动态ES风险测度。实证结果表明，沪深股市在短期内股指连续暴跌现象时有发生，投资者极度负面情绪会加剧股市的剧烈动荡，当考虑投资者情绪对极端风险的冲击时，MSEPP-EMSI模型能有效的提高对极端风险的概率预测精度及ES预测精度。     

The Constrained Extremal Distribution Selection Method

Engineering design and policy formulation often involve the assessment of the likelihood of future events commonly expressed through a probability distribution. Determination of these distributions is based, when possible, on observational data. Unfortunately, these data are often incomplete, biased, and/or incorrect. These problems are exacerbated when policy formulation involves the risk of extreme events—situations of low likelihood and high consequences. Usually, observational data simply do not exist for such events. Therefore, determination of probabilities which characterize extreme events must utilize all available knowledge, be it subjective or observational, so as to most accurately reflect the likelihood of such events. Extending previous work on the statistics of extremes, the Constrained Extremal Distribution Selection Method is a methodology that assists in the selection of probability distributions that characterize the risk of extreme events using expert opinion to constrain the feasible values for parameters which explicitly define a distribution. An extremal distribution is then "fit" to observational data, conditional that the selection of parameters does not violate any constraints. Using a random search technique, genetic algorithms, parameters that minimize a measure of fit between a hypothesized distribution and observational data are estimated. The Constrained Extremal Distribution Selection Method is applied to a real world policy problem faced by the U.S. Environmental Protection Agency. Selected distributions characterize the likelihood of extreme, fatal hazardous material accidents in the United States. These distributions are used to characterize the risk of large scale accidents with numerous fatalities.     

Applying the Partitioned Multiobjective Risk Method (PMRM) to Portfolio Selection

The analysis of risk-return tradeoffs and their practical applications to portfolio analysis paved the way for Modern Portfolio Theory (MPT), which won Harry Markowitz a 1992 Nobel Prize in Economics. A typical approach in measuring a portfolio's expected return is based on the historical returns of the assets included in a portfolio. On the other hand, portfolio risk is usually measured using volatility, which is derived from the historical variance-covariance relationships among the portfolio assets. This article focuses on assessing portfolio risk, with emphasis on extreme risks. To date, volatility is a major measure of risk owing to its simplicity and validity for relatively small asset price fluctuations. Volatility is a justified measure for stable market performance, but it is weak in addressing portfolio risk under aberrant market fluctuations. Extreme market crashes such as that on October 19, 1987 ("Black Monday") and catastrophic events such as the terrorist attack of September 11, 2001 that led to a four-day suspension of trading on the New York Stock Exchange (NYSE) are a few examples where measuring risk via volatility can lead to inaccurate predictions. Thus, there is a need for a more robust metric of risk. By invoking the principles of the extreme-risk-analysis method through the partitioned multiobjective risk method (PMRM), this article contributes to the modeling of extreme risks in portfolio performance. A measure of an extreme portfolio risk, denoted by f(4), is defined as the conditional expectation for a lower-tail region of the distribution of the possible portfolio returns. This article presents a multiobjective problem formulation consisting of optimizing expected return and f(4), whose solution is determined using Evolver-a software that implements a genetic algorithm. Under business-as-usual market scenarios, the results of the proposed PMRM portfolio selection model are found to be compatible with those of the volatility-based model. However, under extremely unfavorable market conditions, results indicate that f(4) can be a more valid measure of risk than volatility.