Long‐Term Risk: An Operator Approach

We create an analytical structure that reveals the long‐run risk‐return relationship for nonlinear continuous‐time Markov environments. We do so by studying an eigenvalue problem associated with a positive eigenfunction for a conveniently chosen family of valuation operators. The members of this family are indexed by the elapsed time between payoff and valuation dates, and they are necessarily related via a mathematical structure called a semigroup. We represent the semigroup using a positive process with three components: an exponential term constructed from the eigenvalue, a martingale, and a transient eigenfunction term. The eigenvalue encodes the risk adjustment, the martingale alters the probability measure to capture long‐run approximation, and the eigenfunction gives the long‐run dependence on the Markov state. We discuss sufficient conditions for the existence and uniqueness of the relevant eigenvalue and eigenfunction. By showing how changes in the stochastic growth components of cash flows induce changes in the corresponding eigenvalues and eigenfunctions, we reveal a long‐run risk‐return trade‐off.     

Behavioral Economics and Regulatory Analysis

Behavioral economics has captured the interest of scholars and the general public by demonstrating ways in which individuals make decisions that appear irrational. While increasing attention is being focused on the implications of this research for the design of risk‐reducing policies, less attention has been paid to how it affects the economic valuation of policy consequences. This article considers the latter issue, reviewing the behavioral economics literature and discussing its implications for the conduct of benefit‐cost analysis, particularly in the context of environmental, health, and safety regulations. We explore three concerns: using estimates of willingness to pay or willingness to accept compensation for valuation, considering the psychological aspects of risk when valuing mortality‐risk reductions, and discounting future consequences. In each case, we take the perspective that analysts should avoid making judgments about whether values are “rational” or “irrational.” Instead, they should make every effort to rely on well‐designed studies, using ranges, sensitivity analysis, or probabilistic modeling to reflect uncertainty. More generally, behavioral research has led some to argue for a more paternalistic approach to policy analysis. We argue instead for continued focus on describing the preferences of those affected, while working to ensure that these preferences are based on knowledge and careful reflection.     

Ex Ante and Ex Post Values for Changes in Risks

In this paper, I take risk to mean a composite of the probability of an adverse event and the severity of the consequences of the event. I explore two issues in the economic valuation of changes in individual risks brought about by public policies. These are: (1) the relationship between the values of risk prevention (i.e., the lowering of the probabilities of adverse events) and risk reduction (i.e., the reduction of the severity of the consequences of adverse events); and (2) the relationship between ex ante and ex post measures of the value of changes in risk.     

Approximate Generalizations and Computational Experiments

In this paper I demonstrate how one can generalize finitely many examples to statements about (infinite) classes of economic models. If there exist upper bounds on the number of connected components of one‐dimensional linear subsets of the set of parameters for which a conjecture is true, one can conclude that it is correct for all parameter values in the class considered, except for a small residual set, once one has verified the conjecture for a predetermined finite set of points. I show how to apply this insight to computational experiments and spell out assumptions on the economic fundamentals that ensure that the necessary bounds on the number of connected components exist. I argue that these methods can be fruitfully utilized in applied general equilibrium analysis. I provide general assumptions on preferences and production sets that ensure that economic conjectures define sets with a bounded number of connected components. Using the theoretical results, I give an example of how one can explore qualitative and quantitative implications of general equilibrium models using computational experiments. Finally, I show how random algorithms can be used for generalizing examples in high‐dimensional problems.     

Ecological and Economic Risk Analysis of Everglades: Phase I Restoration Alternatives

Evaluating alternatives for restoring the Everglades involves analysis of a complex ecological and economic system for which current knowledge is limited. Uncertain benefits and impacts are analyzed probabilistically in this paper, following otherwise accepted principles of net present value (NPV) analysis. Ecological benefits and impacts were considered in monetary terms. Probabilities for selected uncertain parameters were found by maximizing entropy. The first ecological risk conceptual model for the Everglades ecosystem was developed to show ecological interactions. "Current Plans" for restoration involve discharge of phosphorus-enriched water from artificial wetlands to relatively pristine Everglades marshes for 3–10 years, risking conversion of the ecosystem to a eutrophic cattail marsh. For two of the three areas studied, alternative "Bypass Plans" were shown to avoid the loss of up to 3000 acres of sawgrass marsh at a cost that is probabilistically justified by the value of the ecosystem preserved. Sensitivity of the results to projected ecological changes, eutrophic marsh valuation, natural marsh valuation, and future values as represented in the discount rate, was examined.     

Systems Resilience for Multihazard Environments: Definition,Metrics, and Valuation for Decision Making

The United Nations Office for Disaster Risk Reduction reported that the 2011 natural disasters, including the earthquake and tsunami that struck Japan, resulted in $366 billion in direct damages and 29,782 fatalities worldwide. Storms and floods accounted for up to 70% of the 302 natural disasters worldwide in 2011, with earthquakes producing the greatest number of fatalities. Average annual losses in the United States amount to about $55 billion. Enhancing community and system resilience could lead to massive savings through risk reduction and expeditious recovery. The rational management of such reduction and recovery is facilitated by an appropriate definition of resilience and associated metrics. In this article, a resilience definition is provided that meets a set of requirements with clear relationships to the metrics of the relevant abstract notions of reliability and risk. Those metrics also meet logically consistent requirements drawn from measure theory, and provide a sound basis for the development of effective decision‐making tools for multihazard environments. Improving the resiliency of a system to meet target levels requires the examination of system enhancement alternatives in economic terms, within a decision‐making framework. Relevant decision analysis methods would typically require the examination of resilience based on its valuation by society at large. The article provides methods for valuation and benefit‐cost analysis based on concepts from risk analysis and management.     

Consumption of Bovine Spongiform Encephalopathy (BSE) Contaminated Beef and the Risk of Variant Creutzfeldt‐Jakob Disease

To date, the variant Creutzfeldt‐Jakob disease (vCJD) risk assessments that have been performed have primarily focused on predicting future vCJD cases in the United Kingdom, which underwent a bovine spongiform encephalopathy (BSE) epidemic between 1980 and 1996. Surveillance of potential BSE cases was also used to assess vCJD risk, especially in other BSE‐prevalent EU countries. However, little is known about the vCJD risk for uninfected individuals who accidentally consume BSE‐contaminated meat products in or imported from a country with prevalent BSE. In this article, taking into account the biological mechanism of abnormal prion PrP^res aggregation in the brain, the probability of exposure, and the expected amount of ingested infectivity, we establish a stochastic mean exponential growth model of lifetime exposure through dietary intake. Given the findings that BSE agents behave similarly in humans and macaques, we obtained parameter estimates from experimental macaque data. We then estimated the accumulation of abnormal prions to assess lifetime risk of developing clinical signs of vCJD. Based on the observed number of vCJD cases and the estimated number of exposed individuals during the BSE epidemic period from 1980 to 1996 in the United Kingdom, an exposure threshold hypothesis is proposed. Given the age‐specific risk of infection, the hypothesis explains the observations very well from an extreme‐value distribution fitting of the estimated BSE infectivity exposure. The current BSE statistics in the United Kingdom are provided as an example.     

Altruistic and Private Values For Saving Lives With an Oyster Consumption Safety Program

We use data from an Internet-based survey and estimate the benefits of an oyster consumption safety policy with the contingent valuation method. In addition to providing a context-specific estimate of willingness-to-pay for oyster safety, we consider an important issue in the contingent valuation mortality risk reduction literature. A number of studies find that willingness-to-pay for mortality risk reduction is not sensitive to the scope of the risk change. We present the scope test as a difference in the number of lives saved by the program, instead of small changes in risk, and find that referendum votes are responsive to scope. A third feature of this article is that we identify those at-risk respondents who would most benefit from the policy and decompose willingness-to-pay into use values and altruistic nonuse values. We find that willingness-to-pay per life saved ranges from $3.95 million to $7.69 million for the private good of lives saved when the respondent is at risk (i.e., use values). Willingness-to-pay per life saved including both use and altruistic nonuse values ranges from $6.89 million to $12.87 million.     

中小企业违约风险系统性和异质性测度——基于违约风险成分分析法的研究

与大中型企业相比,经济环境恶化或突发事件冲击使中小企业资产价值更易大幅下降,不仅单个企业违约风险急增,企业间的违约相关性也明显变大。然而不同类型中小企业违约风险变化特征仍有较大差异。为了更好测度中小企业违约风险、分析其相关性和差异性,本文在资产价值满足跳-扩散过程假定下,将或有权益分析法、组合违约风险分析与系统波动风险测度β相结合,把违约风险分解为系统成分和异质成分。系统成分越大,表明企业违约风险越易受外部经济环境和相关违约风险影响。异质成分越大则表明企业违约风险与自身异质性特征更为相关。实证研究表明,违约风险成分分析能较好解释中小企业违约风险的相关性和差异性,有助于违约风险分类管理。     

Customer‐Base Concentration and Inventory Efficiencies: Evidence from the Manufacturing Sector

What is the link between customer‐base concentration and inventory efficiencies in the manufacturing sector? Using hand‐collected data from 10‐K Filings, we find that manufacturers with more concentrated customer bases hold fewer inventories for less time and are less likely to end up with excess inventories, as indicated by the lower likelihood and magnitude of inventory write‐downs and reversals. Using disaggregated inventory disclosures, we find that inventory efficiencies primarily flow through the finished goods inventory account, while raw material efficiencies are offset by higher work‐in‐process holdings and longer work‐in‐process cycles. In additional analysis, we document a valuation premium for more concentrated manufacturers after controlling for other firm characteristics, including default risk and cost of capital estimates. We conclude that investors trade off the costs and benefits of relationships with a limited number of major customers and, on balance, consider customer‐base concentration as a net positive for firm valuation. Overall, our study adds to interdisciplinary research in accounting and operations management by shedding new light on the relevance of major customer disclosures for fundamental analysis and valuation in the manufacturing sector.     

Transform Analysis and Asset Pricing for Affine Jump‐diffusions

In the setting of ‘affine’ jump‐diffusion state processes, this paper provides an analytical treatment of a class of transforms, including various Laplace and Fourier transforms as special cases, that allow an analytical treatment of a range of valuation and econometric problems. Example applications include fixed‐income pricing models, with a role for intensity‐based models of default, as well as a wide range of option‐pricing applications. An illustrative example examines the implications of stochastic volatility and jumps for option valuation. This example highlights the impact on option ‘smirks’ of the joint distribution of jumps in volatility and jumps in the underlying asset price, through both jump amplitude as well as jump timing.     

Managing Demand Risk in Tactical Supply Chain Planning for a Global Consumer Electronics Company

We consider the problem of managing demand risk in tactical supply chain planning for a particular global consumer electronics company. The company follows a deterministic replenishment‐and‐planning process despite considerable demand uncertainty. As a possible way to formally address uncertainty, we provide two risk measures, “demand‐at‐risk” (DaR) and “inventory‐at‐risk” (IaR) and two linear programming models to help manage demand uncertainty. The first model is deterministic and can be used to allocate the replenishment schedule from the plants among the customers as per the existing process. The other model is stochastic and can be used to determine the “ideal” replenishment request from the plants under demand uncertainty. The gap between the output of the two models as regards requested replenishment and the values of the risk measures can be used by the company to reallocate capacity among different products and to thus manage demand/inventory risk.     

Real options valuation principle in the multi-period base-stock problem

This paper analyzes the multi-period base-stock problem where there is a financial risk associated with a stochastic demand. For the single-period problem, it is known that the optimal inventory policy can be obtained with the Black and Scholes option pricing formula. This paper pushes the analysis further by applying the options valuation framework to the multi-period problem and presenting an algorithm for finding the optimal inventory policy. A computational study indicates that the effect of systematic risk is typically negligible (as for the single-period problem). Therefore, it can be concluded that systematic risk in demand is of little importance for optimal inventory control.     

Optimal Taxes on Fossil Fuel in General Equilibrium

We analyze a dynamic stochastic general‐equilibrium (DSGE) model with an externality—through climate change—from using fossil energy. Our central result is a simple formula for the marginal externality damage of emissions (or, equivalently, for the optimal carbon tax). This formula, which holds under quite plausible assumptions, reveals that the damage is proportional to current GDP, with the proportion depending only on three factors: (i) discounting, (ii) the expected damage elasticity (how many percent of the output flow is lost from an extra unit of carbon in the atmosphere), and (iii) the structure of carbon depreciation in the atmosphere. Thus, the stochastic values of future output, consumption, and the atmospheric CO₂ concentration, as well as the paths of technology (whether endogenous or exogenous) and population, and so on, all disappear from the formula. We find that the optimal tax should be a bit higher than the median, or most well‐known, estimates in the literature. We also formulate a parsimonious yet comprehensive and easily solved model allowing us to compute the optimal and market paths for the use of different sources of energy and the corresponding climate change. We find coal—rather than oil—to be the main threat to economic welfare, largely due to its abundance. We also find that the costs of inaction are particularly sensitive to the assumptions regarding the substitutability of different energy sources and technological progress.     

Returns Policy and Quality Risk in E‐Business

In this article, we investigate the interplay between returns policy, pricing strategy, and quality risk. We define quality risk as the possibility of product misfit, defect, or unconformity with the consumers’ perception. These notions of quality risks differ in return policy restriction, residual values, and whether it is possible to unambiguously reduce the probability of mismatch. Using a stylized two‐segment market setting, we demonstrate that consumer returns are offered only when the high‐segment consumers incur a higher hassle cost, and both the quality risk and the valuation of the low segment are moderate. Moreover, it is possible to wisely design the returns policy that eliminates all inappropriate returns. Furthermore, the seller with a high‐quality risk may offer a refund that exceeds the selling price, which provides a theoretical ground and specific operating regime for the satisfaction guaranteed policy used in some e‐tailers. In contrast, when the quality risk is relatively low, further improvement on mitigating the quality risk may not necessarily benefit the seller. Finally, we observe that the restocking fee may be non‐monotonic in product quality; thus, a more generous returns policy does not necessarily indicate a lower quality risk.     

系统性风险约束下的商业银行成本、利润效率比较研究

本文基于16家中国上市银行2006~2012年的非平衡面板数据,运用随机边界分析方法,对系统性风险约束下的银行成本、利润效率及其无效率效应进行了比较研究。结果发现:中国银行业的风险主要来源于系统性风险;不考虑风险因素将导致效率值的明显低估;在成本、利润效率模型中,系统性风险越高,其所造成的无效率效应越大。加强风险管理,防止系统性风险的爆发,有利于商业银行效率的提高。     

Construction Safety Risk Modeling and Simulation

By building on a genetic‐inspired attribute‐based conceptual framework for safety risk analysis, we propose a novel approach to define, model, and simulate univariate and bivariate construction safety risk at the situational level. Our fully data‐driven techniques provide construction practitioners and academicians with an easy and automated way of getting valuable empirical insights from attribute‐based data extracted from unstructured textual injury reports. By applying our methodology on a data set of 814 injury reports, we first show the frequency‐magnitude distribution of construction safety risk to be very similar to that of many natural phenomena such as precipitation or earthquakes. Motivated by this observation, and drawing on state‐of‐the‐art techniques in hydroclimatology and insurance, we then introduce univariate and bivariate nonparametric stochastic safety risk generators based on kernel density estimators and copulas. These generators enable the user to produce large numbers of synthetic safety risk values faithful to the original data, allowing safety‐related decision making under uncertainty to be grounded on extensive empirical evidence. One of the implications of our study is that like natural phenomena, construction safety may benefit from being studied quantitatively by leveraging empirical data rather than strictly being approached through a managerial perspective using subjective data, which is the current industry standard. Finally, a side but interesting finding is that in our data set, attributes related to high energy levels (e.g., machinery, hazardous substance) and to human error (e.g., improper security of tools) emerge as strong risk shapers.     

Dread and Risk Elimination Premium for the Value of a Statistical Life

The value of a statistical life (VSL) is a widely used measure for the value of mortality risk reduction. As VSL should reflect preferences and attitudes to risk, there are reasons to believe that it varies depending on the type of risk involved. It has been argued that cancer should be considered a “dread disease,” which supports the use of a “cancer premium.” The objective of this study is to investigate the existence of a cancer premium (for pancreatic cancer and multiple myeloma) in relation to road traffic accidents, sudden cardiac arrest, and amyotrophic lateral sclerosis (ALS). Data were collected from 500 individuals in the Swedish general population of 50–74‐year olds using a web‐based questionnaire. Preferences were elicited using the contingent valuation method, and a split‐sample design was applied to test scale sensitivity. VSL differs significantly between contexts, being highest for ALS and lowest for road traffic accidents. A premium (92–113%) for cancer was found in relation to road traffic accidents. The premium was higher for cancer with a shorter time from diagnosis to death. A premium was also found for sudden cardiac arrest (73%) and ALS (118%) in relation to road traffic accidents. Eliminating risk was associated with a premium of around 20%. This study provides additional evidence that there exist a dread premium and risk elimination premium. These factors should be considered when searching for an appropriate value for economic evaluation and health technology assessment.     

Trend effects on perceived avalanche hazard

Hazard-level forecasts constitute an important risk mitigation tool to reduce loss of economic values and human life. Avalanche forecasts represent an example of this. As for many other domains, avalanche risk is communicated using a color-coded, categorical risk scale aimed at informing the public about past, current, and future risk. We report the results from three experiments in which we tested if an irrelevant past trend in forecasted avalanche danger affects perceptions of current and future avalanche risk. Our sample consisted of individuals from three different populations targeted by national avalanche warning services. All three experiments showed that the perception of avalanche risk is influenced by the trend, but that the effect is opposite for perceptions of current and expectations of future avalanche risk. While future avalanche risk is extrapolated in the same direction as the change from the previous day, we found that perceived current risk appears to be based on an average of past and current risk. These effects diminish when we provide participants with a scale indicating the exact level of avalanche danger. For most of our measurement instruments, however, the effects remain significant. These results imply that targeted populations may consider historic information more than was intended by the sender. As such, our results have implications for both avalanche warning services and risk communication in general.