Risk Of Rare Events Research Articles

Rare and extreme outcomes in risky choice

Many real-world decisions involving rare events also involve extreme outcomes. Despite this confluence, decisions-from-experience research has only examined the impact of rarity and extremity in isolation. With rare events, people typically choose as if they underestimate the probability of a rare outcome happening. Separately, people typically overestimate the probability of an extreme outcome happening. Here, for the first time, we examine the confluence of these two biases in decisions-from-experience. In a between-groups behavioural experiment, we examine people’s risk preferences for rare extreme outcomes and for rare non-extreme outcomes. When outcomes are both rare and extreme, people’s risk preferences shift away from traditional risk patterns for rare events: they show reduced underweighting for events that are both rare and extreme. We simulate these results using a small-sample model of decision-making that accounts for both the underweighting of rare events and the overweighting of extreme events. These separable influences on risk preferences suggest that to understand real-world risk for rare events we must also consider the extremity of the outcomes.

Social Security safety net with rare event risk

AbstractThe US Social Security program was created in part as an explicit response to the Great Depression. We evaluate the performance of Social Security as a protective safety net against a rare episode of sudden and significant loss of private wealth such as the Great Depression. We construct a model in which a rare event causes a shock to wealth at an unknown time. How well does Social Security function as a safety net against such risk? The answer depends critically on whether households optimize in the face of this risk. If the household has full information on the distribution of rare event risk and solves a dynamic stochastic problem to hedge this risk, then Social Security is unnecessary along this dimension. Alternatively, if the household does not account for rare event risk in its financial planning, then Social Security can provide very large welfare gains as a safety net.

Graphical Models for Extremes

SummaryConditional independence, graphical models and sparsity are key notions for parsimonious statistical models and for understanding the structural relationships in the data. The theory of multivariate and spatial extremes describes the risk of rare events through asymptotically justified limit models such as max-stable and multivariate Pareto distributions. Statistical modelling in this field has been limited to moderate dimensions so far, partly owing to complicated likelihoods and a lack of understanding of the underlying probabilistic structures. We introduce a general theory of conditional independence for multivariate Pareto distributions that enables the definition of graphical models and sparsity for extremes. A Hammersley–Clifford theorem links this new notion to the factorization of densities of extreme value models on graphs. For the popular class of Hüsler–Reiss distributions we show that, similarly to the Gaussian case, the sparsity pattern of a general extremal graphical model can be read off from suitable inverse covariance matrices. New parametric models can be built in a modular way and statistical inference can be simplified to lower dimensional marginals. We discuss learning of minimum spanning trees and model selection for extremal graph structures, and we illustrate their use with an application to flood risk assessment on the Danube river.

Rare event risk analysis – application to iceberg collision

To design an engineering system, testing in extreme conditions is at least recommended if not required. There are ambiguities about how to define an extreme state and how to consider it in the design of a system or its operation. The probability estimation of such an event is challenging due to data scarcity, especially in many engineering domains, e.g. offshore development. In this study, available techniques for analyzing the probability of extreme events are examined for their suitability in engineering applications, and a framework is proposed for rare event risk analysis. The framework is comprised of three phases. In the first phase, the outlier based extreme value theory is implemented to estimate the rare event probability. The maximum likelihood criterion is used to estimate the extreme distribution parameters. In the second phase, the rare event is considered as a heavy tail event, and the tail index is estimated through the Hill and the SmooHill estimator. In the third phase, The uncertainty analysis is conducted, and the risk is computed. The proposed methodology is tested for extreme iceberg risk assessment on large offshore structures in the Flemish Pass basin. For this specific case, the estimated design extreme iceberg speed was 4.31 km/h, with an occurrence probability of 3.61E-06.

Patient and surgery factors associated with the incidence of failed and difficult intubation.

Estimates of the rate and risk-factors for difficult airway rarely include a denominator for the number of anaesthetics. Approaches such as self-reporting and crowd-sourcing of airway incidents may help identify specific lessons from clinical episodes, but the lack of denominator data, biased reporting and under-reporting does not allow a comprehensive population-based assessment. We used an established state-wide dataset to determine the incidence of failed and difficult intubations between 2015 and 2017 in the state of Victoria in Australia, along with associated patient and surgical risk-factors. A total of 861,533 general anaesthesia episodes were analysed. Of these, 4092 patients with difficult or failed intubation were identified; incidence rates of 0.52% (2015-2016) and 0.43% (2016-2017), respectively. Difficult/failed intubations were most common in patients aged 45-75 and decreased for older age groups, with risk being lower for patients aged>85 than patients aged 35-44. The risk for failed/difficult intubation increased significantly for: patients undergoing emergency surgery (OR 1.80); obese patients (OR 2.48); increased ASA physical status; and increased Charlson Comorbidity Index. Across all age groups, procedures on the nervous system (OR 1.92) and endocrine system (OR 2.03) had the highest risk of failed/difficult intubation. The relative reduced risk for failed/difficult intubations in the elderly population is a novel finding that contrasts with previous research and may suggest a 'compression of morbidity' effect as a moderator. Administrative databases have the potential to improve understanding of peri-operative risk of rare events at a population level.

Subjective Risk Estimation of the Rare Event

Abstract In the safety engineering, the most frequently disadvantage in risk estimation is the lack of data. In such cases, we have to rely on subjective estimations made by persons with practical knowledge in the field of interest, i.e. experts. However, in some realistic situations, they may have uncertainty in the perceiving and evaluation of the problem considered or limited knowledge of the rare events, such as the consequences of the seagoing ship propulsion failures. The probabilistic models of the risk estimation turn out to be insufficient in modelling the subjective uncertainty. The fuzzy methods are viewed to be powerful in dealing with ambiguity and uncertainty that can be used to handle with the subjective estimation. This article addresses the intuitionistic fuzzy method in the subjective estimation of the ship propulsion failure consequences as rare event risk. In the article, a subjective model of the ship propulsion risk is developed as scenarios of the different subsequent consequences of loss of ship propulsion function until a seriously severe accident resulting in loss of seaworthiness. The model proposes an approach combining AHP method and intuitionistic fuzzy method to assess the occurrence probability and severe probability of these rare events based on the expert opinions. In order to show the applicability of the proposed model, a study case of the propulsion risk of the container carrier operating on the North Atlantic lines is conducted.

The assessment of probabilities and risk of rare events in electric power industry

Issues related to the assessment of probabilities for significant but rare events, extreme and catastrophic situations in the electric power industry are herein examined and analyzed. Special attention is paid to methods of the quantitative assessment of technological risk and its factors. Certain examples are given.

What Drives the Consumer Credit Spread? An Explanation Based on Rare Event Risk and Belief Dispersion

What drives consumers borrowing/lending and the credit spread over their debt? This paper offers a novel explanation based on rare event risk and belief dispersion in a dynamic general equilibrium model. Heterogeneous beliefs drive consumers to borrow, but the market is incomplete and subject to rare event risk and thus default endogenously occurs in equilibrium. The paper derives the credit spread in closed form and yields a credit spread similar to real data when the model is calibrated. The model also well captures the relationship between belief dispersion, risk-free rate and credit spread. It shows that belief dispersion, rare event risk and wealth distribution together drive both credit spread and risk-free rate. An increase in either rare event risk or belief dispersion leads to a higher credit spread and a lower risk-free rate. However, the underlying mechanisms are quite different, as the former (rare event risk) is due to substitution effect while the latter (belief dispersion) is due to wealth effect. The paper also makes a contribution to the literature on rare disaster by endogenizing default and clarifies Barro(2006)'s argument on the countervailing effects of rare disasters on interest rates.

Frequência e risco sob não-estacionariedade em registros pluviométricos da bacia do alto rio Tarauacá, Acre

Nonstationary trends in hydrological time series have aroused the interest of experts in recent decades. Consequently, conventional methods used for frequency analysis and quantification of risk associated with the occurrence of extreme climate events require adjustment. This study aims to perform the frequency analysis and the quantification of the risk of precipitation for a ten-day period in Tarauaca - Acre, Brazil. The results have shown that nonstationary Gumbel distribution with time-dependent location and scale best fits the observed data, thus allowing the most reliable measurements for risk of rare events, and determining reference quantiles associated with planning horizons or design of hydraulic structures.

IMPROVED DETECTION OF RARE-EVENT RISK OF A PORTFOLIO WITH U.S. REITs

In measuring the market risks of a portfolio, value-at-risk (VaR) is one of the most commonly used tools. In this paper, the copula-generalized autoregressive conditional heteroskedasticity (GARCH) method is used to determine whether it is a better alternative for estimating the VaR of portfolios containing U.S. real estate investment trusts (REITs). The FTSE NAREIT US Real Estate Index, all REITs and the S&P 500 index are used to construct a portfolio. In total, 2800 daily data covering the period of the subprime mortgage crisis of 2007–2009 are used in this paper. We used six constant and two time-varying copula models combined with two GARCH models to form sixteen copula-GARCH models to depict the joint distribution of the two assets in the portfolio. We then computed corresponding one-day VaRs. Compared with the traditional VaR models, our results showed that the time-varying symmetrized Joe–Clayton (SJC) copula model combined with the GARCH Student-t innovation (tvSJC-copula–GARCHt) performed the best, regardless of the market situation. Hence, it could be served as a better way of detecting rare-event risk.

Heterogeneous Beliefs About Rare Event Risk in the Lucas Orchard

This paper investigates the asset pricing implications of investor disagreement about the likelihood of a systematic disaster. I specify a general equilibrium model with multiple trees and heterogeneous beliefs about rare event risk, to understand how risk-sharing mechanisms affect equity and variance risk premia, at an aggregate level and in the cross-section of stock returns. I identify a state dependent link between equity and variance premia, that changes with the distribution of agent consumption. Empirically, as in the model, the variance premium’s predictive power for future excess returns is greater during times of financial distress, mainly for small stocks.

Estimating Endangered Species Interaction Risk With the Kalman Filter

AbstractTo address the tradeoff between biodiversity conservation in marine ecosystems and fishing opportunity, it is important to quantify the risk of endangered species interactions in commercial fisheries. We propose a Kalman filter suitable for rare events to estimate the endangered leatherback turtle take risk in the California drift gillnet fishery in the years 1990–2010, conditional on spatiotemporal factors that affect take rates. Results suggest interaction risk has remained stable, but with substantial variation over the spatiotemporal distribution of effort. Our methods might also apply to recreation demand analysis with rare event risk, or to applications involving irregularly spaced observations, like trade‐level stock market data.

Financial Seismic Risk Analysis of Building Portfolios

The role of financial seismic risk analysis and risk quantification has grown rapidly in dealing with important risk-management decisions for building portfolios. Recent developments in regional seismicity modeling, ground-motion modeling of spatially correlated seismic effects, and seismic fragility analysis have enabled more accurate estimation of earthquake risk exposure of building portfolios. The result from quantitative seismic loss estimation can be represented by a seismic loss curve and various scalar risk metrics, such as annual expected loss, value at risk, and tail value at risk, which are all expressed in monetary terms. Their use facilitates the risk-based decision making and risk communication. This study illustrates the current risk-quantification approaches through a case study for a group of wood-frame houses in Canada. Potential pitfalls in using simple risk metrics for decision analysis on seismic risk-transfer and risk-mitigation strategies are discussed. The results indicate that the use of tail value at risk may be appropriate as it provides more consistent risk-comparison results by reflecting the expected risk of rare events.

Modeling Rare Events: Using a Fixed/Variable Rate Model for an Arctic Oil Spill Rate Example

:Occurrence rates for rare events must often be estimated with limited data of unknown and changing applicability; thus, many risk models rely on average measures of risk even though more accurate possibilities may exist. A generalized approach is presented for selecting the best model of the rare event risk and for matching how the results are presented to decision-making needs. The process is illustrated using a case study of estimating oil spill rates from undersea pipelines that serve production platforms on the Outer Continental Shelf areas of the Gulf of Mexico. Existing models use average oil spill rates from these undersea pipelines, but many of these spills occur at a platform; thus, a new approach using a fixed/variable rate framework is suggested. We review the literature on modeling of Outer Continental Shelf oil spill rates, analyze historical oil spills for the estimated rates for both models, and contrast the results (that can differ by up to a factor of 2) for Arctic applications. Other quantitative applications for deeper, more distant wells in the Gulf of Mexico, air and spacecraft flights, maintenance of nuclear facilities, and failure of project activities are suggested. The proposed model is based on estimating average rates for the fixed and variable components. This model is placed on a continuum of risk models based on their data requirements, which provides a new conceptual framework for risk model “levels.” Implications for qualitative mental models of risk are also suggested; thus, there are many potential applications in risk models used by managers and operators.

Rare event risk and emerging market debt with heterogeneous beliefs

In a setting where the lender and the borrower have heterogeneous beliefs about the likelihood of a disastrous shock to the borrower's economy, we study the debt contract that defaults at the occurrence of that shock, as proposed by Barro (2006). We find that a higher belief by the lender compared to the borrower can lead to countercyclical interest rates and credit spreads in non-default times, and to an increase in the borrower's indebtedness in default times, as often observed in emerging market economies. When calibrating the model to prices in the credit default swap market, we show that heterogeneous beliefs can account for more than 40% of the variation in CDS spreads associated with shocks to the borrower's economy in non-default times.

Response to Vieweg and Hasnain Letter

Back to table of contents Previous article Next article Communications and UpdatesFull AccessResponse to Vieweg and Hasnain LetterBrian L. Strom, M.D., M.P.H.Brian L. StromPhiladelphia, Pa.Search for more papers by this author, M.D., M.P.H.Published Online:1 Jun 2011https://doi.org/10.1176/appi.ajp.2011.11020288rAboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InEmail To the Editor: We appreciate the interest of Drs. Vieweg and Hasnain in our work and the opportunity to be explicit about what the goal of our study was. Drs. Vieweg and Hasnain are concerned that our data may be misconstrued, claiming that we “may have inferred conclusions about ziprasidone and QTc interval prolongation that are not supported by the data.” However, as indicated in our title and throughout the article (1), our goal was to look at comparative rates of nonsuicide mortality. The conclusion of our abstract is explicit: “the study was neither powered nor designed to examine the risk of rare events like torsade de pointes.” The article ends with the following:However, this study was not powered to examine the risk of an extremely rare event like torsade de pointes, which would have required a sample size that was orders of magnitude larger than the 18,154 patients examined in ZODIAC and would have required intensive and prolonged cardiac monitoring, which would have been at odds with the study's goal of adhering to routine clinical care.Thus, we were not studying QTc prolongation and indeed did not even measure it. There has never been any question that ziprasidone prolongs QTc, based on Pfizer's clinical data (2). Our goal was to see whether that led to an increase in nonsuicide mortality.Finally, Drs. Vieweg and Hasnain propose looking at case reports as a way to answer the question they pose, referencing two that they published. While case reports have their place in studying adverse drug reactions (3, 4), they could not have answered the question we were addressing. Furthermore, it is important to keep in mind their substantial limitations. As has often been stated, “The plural of anecdote is not data.”Philadelphia, Pa.The author's disclosures accompany the original article.Accepted for publication in March 2011.

The rare event risk in African emerging stock markets

PurposeThe purpose of this paper is to investigate the asymptotic distribution of the extreme daily stock returns in African stock markets over the period 1996‐2007 and examine the implications for downside risk measurement.Design/methodology/approachExtreme value theory methods are used to model adequately the extreme minimum daily returns in a number of African emerging stock markets.FindingsThe empirical results indicate that the generalised logistic distribution best fitted the empirical data over the period of study.Practical implicationsUsing the generalised extreme value and normal distributions for risk assessment could lead to an underestimation of the likelihood of extreme share price declines which could potentially lead to inadequate protection against catastrophic losses.Originality/valueTo the best of the author's knowledge, this is the first study to examine the lower tail distribution of daily returns for African emerging stock markets.

Rare Event Risk and Heterogeneous Beliefs: The Case of Incomplete Markets

This paper provides an equilibrium model subject to heterogeneous beliefs about the likelihood of rare events. I explore asset pricing implications in an incomplete capital market and the effects of market completion. Without explicit rare event insurance, investors insure themselves indirectly through the stock and money markets, the risk premium is countercyclical, and flight to quality effects arise. Upon market completion, the risk premium increases as investors increase their exposure to rare event risk. While market completion leads to a more efficient allocation based on investors’ anticipatory utilities, its effect on ex post efficiency is ambiguous.

Comparative Mortality Associated With Ziprasidone and Olanzapine in Real-World Use Among 18,154 Patients With Schizophrenia: The Ziprasidone Observational Study of Cardiac Outcomes (ZODIAC)

The authors compared 1-year mortality rates associated with ziprasidone and olanzapine in real-world use. The Ziprasidone Observational Study of Cardiac Outcomes (ZODIAC) was an open-label, randomized, postmarketing large simple trial that enrolled patients with schizophrenia (N=18,154) in naturalistic practice in 18 countries. The primary outcome measure was nonsuicide mortality in the year after initiation of assigned treatment. Patients were randomly assigned to receive treatment with either ziprasidone or olanzapine and followed for 1 year by unblinded investigators providing usual care. A physician-administered questionnaire was used to collect baseline demographic information, medical and psychiatric history, and concomitant medication use. Follow-up information on hospitalizations and emergency department visits, patients' vital status, and current antipsychotic drug status was collected and reported by treating psychiatrists. Post hoc analyses of sudden death, a secondary endpoint, were also conducted. The incidence of nonsuicide mortality within 1 year of initiating pharmacotherapy was 0.91 for ziprasidone (N=9,077) and 0.90 for olanzapine (N=9,077). The relative risk was 1.02 (95% CI=0.76-1.39). This finding was confirmed in numerous secondary and sensitivity analyses. Despite the known risk of QTc prolongation with ziprasidone treatment, the findings of this study failed to show that ziprasidone is associated with an elevated risk of nonsuicidal mortality relative to olanzapine in real-world use; the study excludes a relative risk larger than 1.39 with a high probability. However, the study was neither powered nor designed to examine the risk of rare events like torsade de pointes.

Measurement Model of Risk Compensation: Evidences from Asian Emerging Markets

This study investigates the measurement of investment weight adjustment on jump risk of five Asian emerging markets. Considering the risk of rare event, we develop a stochastic jump-diffusion model for dynamic asset allocation in an international diversified portfolio. This paper contributes to finding the optimal weight on jump risks that differs from prior research by calculating the jump size and event arrival frequencies. A covariance of international assets investment is obtained by simulating the price process and constructing multiple-dimension jump diffusion on weight adjustment. We also show how to diversify the jump risks by using international assets portfolios in Asian emerging markets.