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.     

A Solar-Centric Approach to Improving Estimates of Exposure Processes for Coronal Mass Ejections

We present a solar-centric approach to estimating the probability of extreme coronal mass ejections (CME) using the Solar and Heliospheric Observatory (SOHO)/Large Angle and Spectrometric Coronagraph Experiment (LASCO) CME Catalog observations updated through May 2018 and an updated list of near-Earth interplanetary coronal mass ejections (ICME). We examine robust statistical approaches to the estimation of extreme events. We then assume a variety of time-independent distributions fitting, and then comparing, the different probability distributions to the relevant regions of the cumulative distributions of the observed CME speeds. Using these results, we then obtain the probability that the velocity of a CME exceeds a particular threshold by extrapolation. We conclude that about 1.72% of the CMEs recorded with SOHO LASCO arrive at the Earth over the time both data sets overlap (November 1996 to September 2017). Then, assuming that 1.72% of all CMEs pass the Earth, we can obtain a first-order estimate of the probability of an extreme space weather event on Earth. To estimate the probability over the next decade of a CME, we fit a Poisson distribution to the complementary cumulative distribution function. We inferred a decadal probability of between 0.01 and 0.09 for an event of at least the size of the large 2012 event, and a probability between 0.0002 and 0.016 for the size of the 1859 Carrington event.     

基于重现时间间隔分析的极端收益预测及交易策略研究

极端收益的预测在金融风险管理中非常重要。本文系统研究了极端收益重现时间间隔的统计规律，提出了一种基于重现时间间隔分析的早期预警模型，并对极端收益的重现进行预测，检验了模型在样本内外的预测性能；最后分别针对极端正收益和极端负收益的样本外预测结果，设计了看涨和看跌的两种交易策略，并以中国上证指数、法国CAC40指数、英国富时指数、香港恒生指数和日本日经指数为例，对交易策略的日均收益率进行了统计显著性检验。研究结果表明，极端收益的重现时间间隔具有右偏、尖峰厚尾和强自相关等典型特征；极端收益预测模型在样本内和样本外检验中都具有良好的预测能力；看涨和看跌交易策略在卖出区间均能有效地避开下跌阶段，看涨策略有更显著的盈利水平。     

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.     

A Risk Assessment Framework for the Socioeconomic Impacts of Electricity Transmission Infrastructure Failure Due to Space Weather: An Application to the United Kingdom

Space weather phenomena have been studied in detail in the peer‐reviewed scientific literature. However, there has arguably been scant analysis of the potential socioeconomic impacts of space weather, despite a growing gray literature from different national studies, of varying degrees of methodological rigor. In this analysis, we therefore provide a general framework for assessing the potential socioeconomic impacts of critical infrastructure failure resulting from geomagnetic disturbances, applying it to the British high‐voltage electricity transmission network. Socioeconomic analysis of this threat has hitherto failed to address the general geophysical risk, asset vulnerability, and the network structure of critical infrastructure systems. We overcome this by using a three‐part method that includes (i) estimating the probability of intense magnetospheric substorms, (ii) exploring the vulnerability of electricity transmission assets to geomagnetically induced currents, and (iii) testing the socioeconomic impacts under different levels of space weather forecasting. This has required a multidisciplinary approach, providing a step toward the standardization of space weather risk assessment. We find that for a Carrington‐sized 1‐in‐100‐year event with no space weather forecasting capability, the gross domestic product loss to the United Kingdom could be as high as £15.9 billion, with this figure dropping to £2.9 billion based on current forecasting capability. However, with existing satellites nearing the end of their life, current forecasting capability will decrease in coming years. Therefore, if no further investment takes place, critical infrastructure will become more vulnerable to space weather. Additional investment could provide enhanced forecasting, reducing the economic loss for a Carrington‐sized 1‐in‐100‐year event to £0.9 billion.     

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.     

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.     

A Methodology for Assessing the Probability of Occurrence of Undesired Events in the Tietê–Paraná Inland Waterway Based on Expert Opinion

The market share of Tietê–Paraná inland waterway (TPIW) in the transport matrix of the São Paulo state, Brazil, is currently only 0.6%, but it is expected to increase to 6% over the next 20 years. In this scenario, to identify and explore potential undesired events a risk assessment is necessary. Part of this involves assigning the probability of occurrence of events, which usually is accomplished by a frequentist approach. However, in many cases, this approach is not possible due to unavailable or nonrepresentative data. This is the case of the TPIW that even though an expressive accident history is available, a frequentist approach is not suitable due to differences between current operational conditions and those met in the past. Therefore, a subjective assessment is an option as allows for working independently of the historical data, thus delivering more reliable results. In this context, this article proposes a methodology for assessing the probability of occurrence of undesired events based on expert opinion combined with fuzzy analysis. This methodology defines a criterion to weighting the experts and, using the fuzzy logic, evaluates the similarities among the experts’ beliefs to be used in the aggregation process before the defuzzification that quantifies the probability of occurrence of the events based on the experts’ opinion. Moreover, the proposed methodology is applied to the real case of the TPIW and the results obtained from the elicited experts are compared with a frequentist approach evidencing the impact on the results when considering different interpretations of the probability.     

Fault and Event Tree Analyses for Process Systems Risk Analysis: Uncertainty Handling Formulations

Quantitative risk analysis (QRA) is a systematic approach for evaluating likelihood, consequences, and risk of adverse events. QRA based on event (ETA) and fault tree analyses (FTA) employs two basic assumptions. The first assumption is related to likelihood values of input events, and the second assumption is regarding interdependence among the events (for ETA) or basic events (for FTA). Traditionally, FTA and ETA both use crisp probabilities; however, to deal with uncertainties, the probability distributions of input event likelihoods are assumed. These probability distributions are often hard to come by and even if available, they are subject to incompleteness (partial ignorance) and imprecision. Furthermore, both FTA and ETA assume that events (or basic events) are independent. In practice, these two assumptions are often unrealistic. This article focuses on handling uncertainty in a QRA framework of a process system. Fuzzy set theory and evidence theory are used to describe the uncertainties in the input event likelihoods. A method based on a dependency coefficient is used to express interdependencies of events (or basic events) in ETA and FTA. To demonstrate the approach, two case studies are discussed.     

Bayesian approach for optimal PV system sizing under climate change

This paper proposes a novel statistical approach for optimally sizing a stand-alone photovoltaic (PV) system under climate change. Traditionally, the irradiation profile of a typical day or year is used to size PV systems. However, facing the global warming crisis as well as the fact that no two years would have the same weather condition for a single site, this often makes the traditional way failed in the extreme weather conditions. This paper presents a method to statistically model the trend of climate change year by year and put it into the sizing formula, so that the results are optimal for the current weather condition and confidential for the future as well. Hence, the suitable sizes for the PV array and the number of batteries are obtained by pure computation. This is different from the traditional simulation-based sizing curve method. An economic optimization procedure is also presented. In addition to the capital and maintenance costs, a penalty cost is introduced when service fails. A new statistic-based reliability index, the loss of power probability, in terms of threshold-based Extreme Value Theory is presented. This index indicates the upper bound reliability for applications and provides rich information for many extreme events. A technological and economic comparison among the traditional daily energy balance method, sizing curve method and the proposed approach is conducted to demonstrate the usefulness of the new method.     

Geographic Distributions of Extreme Weather Risk Perceptions in the United States

Weather and climate disasters pose an increasing risk to life and property in the United States. Managing this risk requires objective information about the nature of the threat and subjective information about how people perceive it. Meteorologists and climatologists have a relatively firm grasp of the historical objective risk. For example, we know which parts of the United States are most likely to experience drought, heat waves, flooding, snow or ice storms, tornadoes, and hurricanes. We know less about the geographic distribution of the perceived risks of meteorological events and trends. Do subjective perceptions align with exposure to weather risks? This question is difficult to answer because analysts have yet to develop a comprehensive and spatially consistent methodology for measuring risk perceptions across geographic areas in the United States. In this project, we propose a methodology that uses multilevel regression and poststratification to estimate extreme weather and climate risk perceptions by geographic area (i.e., region, state, forecast area, and county). Then we apply the methodology using data from three national surveys (n = 9,542). This enables us to measure, map, and compare perceptions of risk from multiple weather hazards in geographic areas across the country.     

The Event: An Underexamined Risk Concept

Some of the terms used in risk assessment and management are poorly and even contradictorily defined. One such term is “event,” which arguably describes the most basic of all risk‐related concepts. The author cites two contemporary textbook interpretations of “event” that he contends are incorrect and misleading. He then examines the concept of an event in A. N. Kolmogorov's probability axioms and in several more‐current textbooks. Those concepts are found to be too narrow for risk assessments and inconsistent with the actual usage of “event” by risk analysts. The author goes on to define and advocate linguistic definitions of events (as opposed to mathematical definitions)—definitions constructed from natural language. He argues that they should be recognized for what they are: the de facto primary method of defining events.     

COVID-19 and business failures: The paradoxes of experience,scale, and scope for theory and practice

In light of growing scholarly works on business failure, across the social science domains, it is surprising that past studies have largely overlooked how extreme environmental shocks and ‘black swan’ events such as those caused by the coronavirus (COVID-19) pandemic and other global crises, can precipitate business failures. Drawing insights from the current literature on business failure and the unfolding event of COVID-19, we highlight the paradoxes posed by novel exogenous shocks (that is, shocks that transcend past experiences) and the implications for SMEs. The pandemic has accelerated the reconfiguration of the relationship between states and markets, increasing the divide between those with political connections and those without, and it may pose new legitimacy challenges for some players even as others seem less concerned by such matters, whilst experiential knowledge resources may be both an advantage and a burden.     

Property Loss Estimation for Wind and Earthquake Perils

This article describes the development of a generic loss assessment methodology, which is applicable to earthquake and windstorm perils worldwide. The latest information regarding hazard estimation is first integrated with the parameters that best describe the intensity of the action of both windstorms and earthquakes on building structures, for events with defined average return periods or recurrence intervals. The subsequent evaluation of building vulnerability (damageability) under the action of both earthquake and windstorm loadings utilizes information on damage and loss from past events, along with an assessment of the key building properties (including age and quality of design and construction), to assess information about the ability of buildings to withstand such loadings and hence to assign a building type to the particular risk or portfolio of risks. This predicted damage information is then translated into risk-specific mathematical vulnerability functions, which enable numerical evaluation of the probability of building damage arising at various defined levels. By assigning cost factors to the defined damage levels, the associated computation of total loss at a given level of hazard may be achieved. This developed methodology is universal in the sense that it may be applied successfully to buildings situated in a variety of earthquake and windstorm environments, ranging from very low to extreme levels of hazard. As a loss prediction tool, it enables accurate estimation of losses from potential scenario events linked to defined return periods and, hence, can greatly assist risk assessment and planning.     

Risk Analysis of Chemical, Biological, or Radionuclear Threats: Implications for Food Security

If the food sector is attacked, the likely agents will be chemical, biological, or radionuclear (CBRN). We compiled a database of international terrorist/criminal activity involving such agents. Based on these data, we calculate the likelihood of a catastrophic event using extreme value methods. At the present, the probability of an event leading to 5,000 casualties (fatalities and injuries) is between 0.1 and 0.3. However, pronounced, nonstationary patterns within our data suggest that the "reoccurrence period" for such attacks is decreasing every year. Similarly, disturbing trends are evident in a broader data set, which is nonspecific as to the methods or means of attack. While at the present the likelihood of CBRN events is quite low, given an attack, the probability that it involves CBRN agents increases with the number of casualties. This is consistent with evidence of "heavy tails" in the distribution of casualties arising from CBRN events.     

非奇次空间动态极值估计的模型与应用

传统EVT方法是从静态的角度,研究超额数据的性质。然而,它没有同时考虑极端数据发生的时间所隐含的充分信息。本文首次在国内提出了非奇次空间动态极值理论(ITD-EVT)的概念,克服了EVT的上述缺陷,在极端数据的基础上考虑了时间因素,并引入多个解释变量,使极值分布的是三个参数为时变的,用二维泊松分布过程建立动态空间模型,是文中一大特色。把TD-EVT运用于极端情况下风险值的估计中,对金融风险管理、资产定价等问题有较大的理论和现实意义。     

Estimating the Probability of Rare Events: Addressing Zero Failure Data

Traditional statistical procedures for estimating the probability of an event result in an estimate of zero when no events are realized. Alternative inferential procedures have been proposed for the situation where zero events have been realized but often these are ad hoc, relying on selecting methods dependent on the data that have been realized. Such data‐dependent inference decisions violate fundamental statistical principles, resulting in estimation procedures whose benefits are difficult to assess. In this article, we propose estimating the probability of an event occurring through minimax inference on the probability that future samples of equal size realize no more events than that in the data on which the inference is based. Although motivated by inference on rare events, the method is not restricted to zero event data and closely approximates the maximum likelihood estimate (MLE) for nonzero data. The use of the minimax procedure provides a risk adverse inferential procedure where there are no events realized. A comparison is made with the MLE and regions of the underlying probability are identified where this approach is superior. Moreover, a comparison is made with three standard approaches to supporting inference where no event data are realized, which we argue are unduly pessimistic. We show that for situations of zero events the estimator can be simply approximated with , where n is the number of trials.     

A Rational Decision Rule with Extreme Events

Risks induced by extreme events are characterized by small or ambiguous probabilities, catastrophic losses, or windfall gains. Through a new functional, that mimics the restricted Bayes-Hurwicz criterion within the Choquet expected utility approach, it is possible to represent the decisionmaker behavior facing both risky (large and reliable probability) and extreme (small or ambiguous probability) events. A new formalization of the precautionary principle (PP) is shown and a new functional, which encompasses both extreme outcomes and expectation of all the possible results for every act, is claimed.