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.     

Modeling Correlated Discrete Uncertainties in Event Trees with Copulas

Modeling the dependence between uncertainties in decision and risk analyses is an important part of the problem structuring process. We focus on situations where correlated uncertainties are discrete, and extend the concept of the copula‐based approach for modeling correlated continuous uncertainties to the representation of correlated discrete uncertainties. This approach reduces the required number of probability assessments significantly compared to approaches requiring direct estimates of conditional probabilities. It also allows the use of multiple dependence measures, including product moment correlation, rank order correlation and tail dependence, and parametric families of copulas such as normal copulas, t‐copulas, and Archimedean copulas. This approach can be extended to model the dependence between discrete and continuous uncertainties in the same event tree.     

国际投资汇率风险的综合套保策略研究

国际组合投资涉及多币种汇率风险,分别使用双边货币期货进行套保要承担较高套保成本。参考美元指数期货的实践,本文提出基于人民币指数期货的综合套保策略。实证结果表明,无论对于单个货币资产还是分散化投资的国际股指、债指组合,引入人民币指数期货能够显著降低收益率波动,提高抵御汇率波动的能力,同时拓展收益空间,是有效的汇率风险综合套保工具;人民币指数期货套保效率显著优于货币期货篮子,在发达国家股指市场表现更加突出。采用基于指数加权移动平均模型（EWMA）的动态套保策略,使得人民币指数期货收益对股指或债指市场波动敏感度降低,在市场极端状况时仍能保持相对中性。     

Risk Finance for Catastrophe Losses with Pareto‐Calibrated Lévy‐Stable Severities

For catastrophe losses, the conventional risk finance paradigm of enterprise risk management identifies transfer, as opposed to pooling or avoidance, as the preferred solution. However, this analysis does not necessarily account for differences between light‐ and heavy‐tailed characteristics of loss portfolios. Of particular concern are the decreasing benefits of diversification (through pooling) as the tails of severity distributions become heavier. In the present article, we study a loss portfolio characterized by nonstochastic frequency and a class of Lévy‐stable severity distributions calibrated to match the parameters of the Pareto II distribution. We then propose a conservative risk finance paradigm that can be used to prepare the firm for worst‐case scenarios with regard to both (1) the firm's intrinsic sensitivity to risk and (2) the heaviness of the severity's tail.     

A Blueprint for Full Collective Flood Risk Estimation: Demonstration for European River Flooding

Floods are a natural hazard evolving in space and time according to meteorological and river basin dynamics, so that a single flood event can affect different regions over the event duration. This physical mechanism introduces spatio‐temporal relationships between flood records and losses at different locations over a given time window that should be taken into account for an effective assessment of the collective flood risk. However, since extreme floods are rare events, the limited number of historical records usually prevents a reliable frequency analysis. To overcome this limit, we move from the analysis of extreme events to the modeling of continuous stream flow records preserving spatio‐temporal correlation structures of the entire process, and making a more efficient use of the information provided by continuous flow records. The approach is based on the dynamic copula framework, which allows for splitting the modeling of spatio‐temporal properties by coupling suitable time series models accounting for temporal dynamics, and multivariate distributions describing spatial dependence. The model is applied to 490 stream flow sequences recorded across 10 of the largest river basins in central and eastern Europe (Danube, Rhine, Elbe, Oder, Waser, Meuse, Rhone, Seine, Loire, and Garonne). Using available proxy data to quantify local flood exposure and vulnerability, we show that the temporal dependence exerts a key role in reproducing interannual persistence, and thus magnitude and frequency of annual proxy flood losses aggregated at a basin‐wide scale, while copulas allow the preservation of the spatial dependence of losses at weekly and annual time scales.     

Integrated Direct and Indirect Flood Risk Modeling: Development and Sensitivity Analysis

In this article, we propose an integrated direct and indirect flood risk model for small‐ and large‐scale flood events, allowing for dynamic modeling of total economic losses from a flood event to a full economic recovery. A novel approach is taken that translates direct losses of both capital and labor into production losses using the Cobb‐Douglas production function, aiming at improved consistency in loss accounting. The recovery of the economy is modeled using a hybrid input‐output model and applied to the port region of Rotterdam, using six different flood events (1/10 up to 1/10,000). This procedure allows gaining a better insight regarding the consequences of both high‐ and low‐probability floods. The results show that in terms of expected annual damage, direct losses remain more substantial relative to the indirect losses (approximately 50% larger), but for low‐probability events the indirect losses outweigh the direct losses. Furthermore, we explored parameter uncertainty using a global sensitivity analysis, and varied critical assumptions in the modeling framework related to, among others, flood duration and labor recovery, using a scenario approach. Our findings have two important implications for disaster modelers and practitioners. First, high‐probability events are qualitatively different from low‐probability events in terms of the scale of damages and full recovery period. Second, there are substantial differences in parameter influence between high‐probability and low‐probability flood modeling. These findings suggest that a detailed approach is required when assessing the flood risk for a specific region.     

A numerical analysis of supply chain performance under split decision rights

We examine periodic review supply chain models where order quantity and shipping frequency are both decision variables and decision-making rights are split between supply chain agents. We address two general questions: (1) when does decentralized decision making result in the greatest loss in supply chain performance; and (2) what effect does the distribution of channel power have on performance loss. We characterize optimal policies where possible in each scenario and we use numerical analysis to generate insights. We find that performance losses from decentralized control are somewhat limited in our results due to risk pooling and that the magnitude of performance loss is strongly influenced by the relative holding and penalty costs, but somewhat invariant to demand uncertainty. Furthermore, we find that concentrating channel power with the supplier can lead to supply chain profits that are very close to a centralized scenario, but also results in lower customer service levels.     

Uncertainty and the Value of Information with Stochastic Losses from Global Warming

We present an uncertainty analysis conducted using CETA-R, a model in which the costs of climate change are specified as Risks of large losses. In this analysis, we assume that three key parameters may each take on "high" or "low" values, leading to eight possible states of the world. We then explore optimal policies when the state of the world is known, and under uncertainty. Also, we estimate the benefits of resolving uncertainty earlier. We find that the optimal policy under uncertainty is similar to the policy that is optimal when each of the key parameters is at its low value. We also find that the value of immediate uncertainty resolution rises sharply as the alternative to immediate resolution is increasingly delayed resolution.     

THE VALUE OF SKU RATIONALIZATION IN PRACTICE (THE POOLING EFFECT UNDER SUBOPTIMAL INVENTORY POLICIES AND NONNORMAL DEMAND)

Several approaches to the widely recognized challenge of managing product variety rely on the pooling effect. Pooling can be accomplished through the reduction of the number of products or stock‐keeping units (SKUs), through postponement of differentiation, or in other ways. These approaches are well known and becoming widely applied in practice. However, theoretical analyses of the pooling effect assume an optimal inventory policy before pooling and after pooling, and, in most cases, that demand is normally distributed. In this article, we address the effect of nonoptimal inventory policies and the effect of nonnormally distributed demand on the value of pooling. First, we show that there is always a range of current inventory levels within which pooling is better and beyond which optimizing inventory policy is better. We also find that the value of pooling may be negative when the inventory policy in use is suboptimal. Second, we use extensive Monte Carlo simulation to examine the value of pooling for nonnormal demand distributions. We find that the value of pooling varies relatively little across the distributions we used, but that it varies considerably with the concentration of uncertainty. We also find that the ranges within which pooling is preferred over optimizing inventory policy generally are quite wide but vary considerably across distributions. Together, this indicates that the value of pooling under an optimal inventory policy is robust across distributions, but that its sensitivity to suboptimal policies is not. Third, we use a set of real (and highly erratic) demand data to analyze the benefits of pooling under optimal and suboptimal policies and nonnormal demand with a high number of SKUs. With our specific but highly nonnormal demand data, we find that pooling is beneficial and robust to suboptimal policies. Altogether, this study provides deeper theoretical, numerical, and empirical understanding of the value of pooling.     

Does Size Matter? A Study of Risk Perceptions of Global Population Growth

The global human population now exceeds 7 billion and is projected to reach 10 billion around 2060. While population growth has been associated with certain benefits (e.g., economies of scale, technological advancements), theoretical models, probabilistic projections, and empirical evidence also indicate that this growth could increase the likelihood of many adverse events (e.g., climate change, resource shortages) and the impact of these events, as more people are exposed to the outcomes. While concerns about these issues are well‐documented in the academic literature, there is little evidence concerning the public's perceptions of the risks associated with global population growth (GPG) and how these perceptions are likely to influence related decisions. To address these issues, we conducted a U.K.‐based study that examined respondents’ risk perceptions of GPG, their willingness to embrace mitigation/precautionary behaviors, and reasons for variations in these two factors. We found that GPG is perceived as a moderate‐to‐high risk, with concerns about the increased likelihood of resource shortages, ecological damage, and violent conflict being foremost. Respondents believed that the worst effects of GPG would arrive around 2050 and would be experienced by the world's poorest people. Respondents who perceived greater levels of risk from GPG were generally those who indicated a greater willingness to embrace mitigation behaviors (e.g., reduce resource consumption) and preventative actions (e.g., support political action to limit growth). We discuss how our findings might be utilized to better manage the potential challenges associated with GPG and we suggest several directions for further research.     

Managing the Risk of Global Climate Catastrophe: An Uncertainty Analysis

Despite much scientific progress over many decades, the nature of global climate change remains highly uncertain, and the possibility of global climate catastrophe is one of the main concerns in public debates about global climate change. In this paper, we present a model which incorporates the risk of climate catastrophe in an analysis of greenhouse gas abatement strategy. In this model, the timing and severity of climate catastrophe are treated probabilistically. The impacts of key uncertainties on optimal policy are analyzed, and the expected values of additional information that reduces the uncertainty associated with the world economy, carbon cycle, climate change, and climate damage are estimated.     

Cross-country risk quantification of extreme wildfires in Mediterranean Europe

We estimate the country-level risk of extreme wildfires defined by burned area (BA) for Mediterranean Europe and carry out a cross-country comparison. To this end, we avail of the European Forest Fire Information System (EFFIS) geospatial data from 2006 to 2019 to perform an extreme value analysis. More specifically, we apply a point process characterization of wildfire extremes using maximum likelihood estimation. By modeling covariates, we also evaluate potential trends and correlations with commonly known factors that drive or affect wildfire occurrence, such as the Fire Weather Index as a proxy for meteorological conditions, population density, land cover type, and seasonality. We find that the highest risk of extreme wildfires is in Portugal (PT), followed by Greece (GR), Spain (ES), and Italy (IT) with a 10-year BA return level of 50'338 ha, 33'242 ha, 25'165 ha, and 8'966 ha, respectively. Coupling our results with existing estimates of the monetary impact of large wildfires suggests expected losses of 162–439 million € (PT), 81–219 million € (ES), 41–290 million € (GR), and 18–78 million € (IT) for such 10-year return period events.

SUMMARY

We model the risk of extreme wildfires for Italy, Greece, Portugal, and Spain in form of burned area return levels, compare them, and estimate expected losses.     

Global Warming Risk Perceptions in India

Few studies have focused on global warming risk perceptions among people in poor and developing countries, who are disproportionately impacted by climate change. This analysis conducts a comprehensive assessment of global warming risk perceptions in India using a national sample survey. Consistent with cultural theory, egalitarianism was positively associated with global warming risk perceptions. In addition, perceived vulnerability and resilience to extreme weather events were also two of the strongest factors associated with global warming risk perceptions. While worry was positively associated with risk perceptions, it accounted for only a small proportion of the variance, unlike studies in developed countries. Finally, the study also collected global warming affective images. The most common responses were “don't know” or “can't say” (25%), followed by “pollution” (21%), “heat” (20%), and “nature” (16%). The study finds that the predictors of global warming risk perceptions among the Indian public are both similar and different than those in developed countries, which has important implications for climate change communication in India.     

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.     

Random Pooling Designs Under Various Structures

Balding et al. (1995) showed that randomizing over the k-set space yields much better pooling designs than the random pooling design without the k-restriction. A natural question arises as to whether a smaller subspace, i.e., a space with more structure, will yield even better results. We take the random subset containment design recently proposed by Macula, which randomizes over a subspace of the k-set space, as our guinea pig to compare with the k-set space. Unfortunately the performance of the subset containment design is hard to analyze and only approximations are given. For a set of parameters, we are able to produce either an exact analysis or very good approximations. The comparisons under these parameters seem to favor the k-set space.     

Strategic Consumer Cooperation in a Name‐Your‐Own‐Price Channel

Supplier reluctance to openly advertise highly discounted products on the Internet has stimulated development of “opaque” name‐Your‐Own‐Price sales channels. Unfortunately (for suppliers), there is significant potential for online consumers to exploit these channels through collaboration in social networks. In this paper, we study three possible forms of consumer collaboration: exchange of bid result information, coordinated bidding, and coordinated bidding with risk pooling. We propose an egalitarian total utility maximizing mechanism for coordination and risk pooling in a bidding club and describe characteristics of consumers for whom participation in the club makes sense. We show that, in the absence of risk pooling, a plausible bidding club strategy using just information exchange gives almost the same benefits to consumers as coordinated bidding. In contrast, coordinated bidding with risk pooling can lead to significantly increased benefits for consumers. The benefits of risk pooling are highest for consumers with a low tolerance to risk. We also demonstrate that suppliers that actively adjust for such strategic consumer behavior can reduce the impact on their businesses and, under some circumstances, even increase revenues.     

The Impact of Portfolio Location Uncertainty on Probabilistic Seismic Risk Analysis

Probabilistic seismic risk analysis is a well‐established method in the insurance industry for modeling portfolio losses from earthquake events. In this context, precise exposure locations are often unknown. However, so far, location uncertainty has not been in the focus of a large amount of research. In this article, we propose a novel framework for treatment of location uncertainty. As a case study, a large number of synthetic portfolios resembling typical real‐world cases were created. We investigate the effect of portfolio characteristics such as value distribution, portfolio size, or proportion of risk items with unknown coordinates on the variability of loss frequency estimations. The results indicate that due to loss aggregation effects and spatial hazard variability, location uncertainty in isolation and in conjunction with ground motion uncertainty can induce significant variability to probabilistic loss results, especially for portfolios with a small number of risks. After quantifying its effect, we conclude that location uncertainty should not be neglected when assessing probabilistic seismic risk, but should be treated stochastically and the resulting variability should be visualized and interpreted carefully.     

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.     

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.     

Income Pooling between Australian Young Adults and Their Parents

We test whether young adults who co‐reside with their parents derive influence over household‐level expenditure by earning income. We propose a new variant of the Engel curve consistent with the Quadratic Almost Ideal Demand System, which allows a simple test of income pooling. Our tests suggest that young adults and parents mostly pool their income — pooling is not rejected for 8 out of 12 expenditure categories. We are more likely to reject income pooling between young adults and their parents in those expenditure categories where the model fit is highest, so our results may be interpreted as an upper bound on income pooling. We also apply our tests to income pooling between husbands and wives and find that pooling holds for 9 out of 12 expenditure categories. We find the opposite relationship with fit — expenditure categories where fit is poor are those where we are most likely to reject income pooling.