Risk-averse Decision Research Articles

On the psychology of poverty.

Poverty remains one of the most pressing problems facing the world; the mechanisms through which poverty arises and perpetuates itself, however, are not well understood. Here, we examine the evidence for the hypothesis that poverty may have particular psychological consequences that can lead to economic behaviors that make it difficult to escape poverty. The evidence indicates that poverty causes stress and negative affective states which in turn may lead to short-sighted and risk-averse decision-making, possibly by limiting attention and favoring habitual behaviors at the expense of goal-directed ones. Together, these relationships may constitute a feedback loop that contributes to the perpetuation of poverty. We conclude by pointing toward specific gaps in our knowledge and outlining poverty alleviation programs that this mechanism suggests.

Risk averse decision making under catastrophic risk

A nonstandard probabilistic setting for modeling of the risk of catastrophic events is presented. It allows random variables to take on infinitely large negative values with non-zero probability, which correspond to catastrophic consequences unmeasurable in monetary terms, e.g. loss of human lives. Thanks to this extension, the safety-first principle is proved to be consistent with traditional axioms on a preference relation, such as monotonicity, continuity, and risk aversion. Also, a robust preference relation is introduced, and an example of a monotone robust preference relation, sensitive to catastrophic events in the sense of Chichilnisky (2002), is provided. The suggested setting is demonstrated in evaluating nuclear power plant projects when the probability of a catastrophe is itself a random variable.

A Social Values Analysis of Parental Decision Making

ABSTRACTSocial values theory was used to examine how parents make decisions for their adolescent children. Social values theory states that decision making for others is based on the social value of an action, leading to a norm for how to decide for others, whereas self decisions are influenced by a number of additional factors. Consistent with a risk-aversion norm, in hypothetical health and safety scenarios parents made more risk-averse decisions for their adolescent children than for themselves. Further, the level of risk and inconvenience affected self decisions more than decisions for one's child. A second study showed that the norm was stronger for decisions for one's child than for oneself and more related to parents’ decisions for their child than for themselves. In sum, parents’ decisions for their children seem to be largely determined by a norm stating how they are supposed to decide, at least in the domain of health and safety. Implications for both the judgment and decision making and parenting literatures are discussed.

Pricing and promised delivery lead time decisions with a risk-averse agent

This paper studies how a risk-averse firm determines promised delivery lead time and price in a circumstance where the market demand depends not only on the selling price but also on the promised delivery lead time. Two scenarios, one in which the price and promised delivery lead time are independent and the other in which the price is promised delivery lead time sensitive, are analysed. Under conditional value-at-risk criterion, we examine how the risk aversion of decision-makers influences the optimal selection of price, promised delivery lead time and the overall utility of a risk-averse decision-maker. Moreover, by conducting comprehensive sensitivity analyses, we investigate the interaction effects of the decision-maker’s risk aversion and different parameters, including the price and lead time elasticity indexes, the inventory costs, as well as the capacity parameters on the optimal decisions and utilities, so as to offer managerial implications for practitioners under time-based competition environment.

Probabilistic Analysis of Marine Fuels in Emission Controlled Areas

This study presents a probabilistic analysis for conventional diesel-fuelled engines, LNG-fuelled engines or dual-fuelled (LNG and diesel) engines to establish which is more optimal for container shipping within emission controlled areas. Variables investigated include uncertainty over future NOx and EE regulations, downtime due to engine failure, limitations to LNG bunkering and fuel prices. Decision analysis given perfect information and risk analysis were used to generate varying scenarios to understand how the optimal decision was affected. The optimal decision for a risk neutral decision maker is to invest in a diesel fuelled engine. With perfect information over future NOx regulations, the optimal decision changes to that of purchasing a LNG-fuelled engine. The model also highlights the importance of risk tolerance to the decision problem. On the whole, the more risk averse decision makers are, the likelier they would consider LNG as an alternative fuel source.

Impact of Risk Aversion on Price and Quality Decisions under Demand Uncertainty via the CARA Utility Function

This paper investigates optimal price and quality decisions of a manufacturer-retailer supply chain under demand uncertainty, in which players are both risk-averse decision makers. The manufacturer determines the wholesale price and quality of the product, and the retailer determines the retail price. By means of game theory, we employ the constant absolute risk aversion (CARA) function to analyze two different supply chain structures, that is, manufacturer Stackelberg model (MS) and retailer Stackelberg model (RS). We then analyze the results to explore the effects of risk aversion of the manufacturer and the retailer upon the equilibrium decisions. Our results imply that both the risk aversion of the manufacturer and the retailer play an important role in the price and quality decisions. We find that, in general, in MS and RS models, the optimal wholesale price and quality decrease with the risk aversion of the manufacturer but increase with the risk aversion of the retailer, while the retail price decreases with the risk aversion of the manufacturer as well as the retailer. We also examine the impact of quality cost coefficient on the optimal decisions. Finally, numerical examples are presented to illustrate the different degree of effects of players’ risk aversion on equilibrium results and to compare results in different models considered.

The optimal sequential information acquisition structure: A rational utility-maximizing perspective

We consider a rational utility maximizer decision maker (DM) who must gather two pieces of information from a set of multidimensional products before making a choice. We analyze the resulting sequential information acquisition process where the DM tries to find the best possible product subject to his information acquisition constraint. In addition, we introduce publicly observable signals that allow the DM to update his expected utility functions following a standard Bayesian learning rule. Even though it seems intuitively plausible to assume that the transmission of positive and credible information may lead DMs to accept any product signaled more eagerly, this paper illustrates how transmitting credible positive information is not sufficient to decrease the rejection probability faced by the information sender on its set of products. A significant difference in product rejection probabilities arises depending on the characteristic on which signals are issued, as will be illustrated numerically for both risk-neutral and risk-averse DMs.

Time consistency and risk averse dynamic decision models: Definition, interpretation and practical consequences

This paper aims at resolving a major obstacle to practical usage of time-consistent risk-averse decision models. The recursive objective function, generally used to ensure time consistency, is complex and has no clear/direct interpretation. Practitioners rather choose a simpler and more intuitive formulation, even though it may lead to a time inconsistent policy. Based on rigorous mathematical foundations, we impel practical usage of time consistent models as we provide practitioners with an intuitive economic interpretation for the referred recursive objective function. We also discourage time-inconsistent models by arguing that the associated policies are sub-optimal. We developed a new methodology to compute the sub-optimality gap associated with a time-inconsistent policy, providing practitioners with an objective method to quantify practical consequences of time inconsistency. Our results hold for a quite general class of problems and we choose, without loss of generality, a CVaR-based portfolio selection application to illustrate the developed concepts.

Buying price of event information in two-action decision problems

Being able to determine in advance whether certain events occur or not enables a decision maker to reduce the uncertainty of a two-action lottery, although the exact outcome of the lottery may still not be known with certainty. This paper studies the a priori value of information in such a decision making environment. Of interest to the decision maker is to compare the value of information about different events in advance of gathering the information. Using buying price as value of information, we show that when information about the occurrence of two different events are offered to a risk neutral decision maker, the event with a greater contribution in absolute value to the expected value of the lottery has higher value in terms of its buying price. For risk averse decision makers, a preference condition needs to be imposed on the set difference of two events to obtain a generic conclusion. We provide several examples that demonstrate the usefulness of these results.

Optimizing the conditional value-at-risk in revenue management

Many service industries use revenue management to balance demand and capacity. The assumption of risk-neutrality lies at the heart of the classical approaches, which aim at maximizing expected revenue. In this paper, we give a comprehensive overview of the existing approaches, most of which were only recently developed, and discuss the need to take risk-averse decision makers into account. We then present a heuristic that maximizes Conditional Value-at-Risk (CVaR). Although CVaR has become increasingly popular in finance and actuarial science due to its beneficial properties, this risk measure has not yet been considered in the context of revenue management. We are able to efficiently solve the optimization problem inherent in CVaR by taking advantage of specific structural properties that allow us to reformulate this optimization problem as a continuous knapsack problem. In order to demonstrate the applicability and robustness of our approach, we conduct a simulation study that shows that the new approach can significantly improve the risk profile in various scenarios.

Integrated Strategic Planning of Global Production Networks and Financial Hedging under Uncertain Demands and Exchange Rates

AbstractIn this paper, we present a multi-stage stochastic programming model that integrates financial hedging decisions into the planning of strategic production networks under uncertain exchange rates and product demands. This model considers the expenses of production plants and the revenues of markets in different currency areas. Financial portfolio planning decisions for two types of financial instruments, forward contracts and options, are represented explicitly by multi-period decision variables and a multi-stage scenario tree. Using an illustrative example, we analyze the impact of exchange-rate and demand volatility, the level of investment expenses and interest rate spreads on capacity location and dimensioning decisions. In particular, we show that, in the illustrative example, the exchange-rate uncertainty cannot be completely eliminated by financial hedging in the presence of demand uncertainty. In this situation, we find that the integrated model can result in better strategic planning decisions for a risk-averse decision maker compared to traditional modeling approaches.

Issues on Integrating Real and Financial Decisions

We study the issue of integrating real and financial decisions in a monopoly firm with risk-averse decision-makers. To that end, we combine the decisions of the firm and of the shareholders in a very simple but robust model, with uncertainty in the real market and CARA preferences. We show the existence of equilibrium either in a competitive and a uncompetitive financial market, though different assumptions are needed in each case. In all situations, access to the financial market leads to risk-sharing and an increase in production, but only the competitive case is Pareto optimal. When either the firm or the outside investors act as leaders, the optimal risk-sharing is distorted to favor the leader. We also discuss the effect that changes on the coefficients of risk aversion have on the equilibrium outcomes.

Quantifying uncertainty in pest risk maps and assessments: adopting a risk-averse decision maker’s perspective

Pest risk maps are important decision support tools when devising strategies to minimize introductions of invasive organisms and mitigate their impacts. When possible management responses to an invader include costly or socially sensitive activities, decision-makers tend to follow a more certain (i.e., risk-averse) course of action. We presented a new mapping technique that assesses pest invasion risk from the perspective of a risk-averse decision maker.We demonstrated the method by evaluating the likelihood that an invasive forest pest will be transported to one of the U.S. states or Canadian provinces in infested firewood by visitors to U.S. federal campgrounds. We tested the impact of the risk aversion assumption using distributions of plausible pest arrival scenarios generated with a geographically explicit model developed from data documenting camper travel across the study area. Next, we prioritized regions of high and low pest arrival risk via application of two stochastic ordering techniques that employed, respectively, first- and second-degree stochastic dominance rules, the latter of which incorporated the notion of risk aversion. We then identified regions in the study area where the pest risk value changed considerably after incorporating risk aversion.While both methods identified similar areas of highest and lowest risk, they differed in how they demarcated moderate-risk areas. In general, the second-order stochastic dominance method assigned lower risk rankings to moderate-risk areas. Overall, this new method offers a better strategy to deal with the uncertainty typically associated with risk assessments and provides a tractable way to incorporate decision-making preferences into final risk estimates, and thus helps to better align these estimates with particular decision-making scenarios about a pest organism of concern. Incorporation of risk aversion also helps prioritize the set of locations to target for inspections and outreach activities, which can be costly. Our results are especially important and useful given the huge number of camping trips that occur each year in the United States and Canada.

Effects of Risk Aversion on the Value of Information in Two-Action Decision Problems

This paper analyzes the value of information in a two-action decision problem where a decision maker is deciding on whether to accept an uncertain investment. We investigate the effects of the decision maker's risk aversion function on the value of information in this setting. We analyze the value of perfect information and the value of partition information where a decision maker with deterministic initial wealth receives information specifying that the outcome lies within a subset of the domain. We show that if two decision makers reject the investment without the information, then the more risk-averse decision maker will value information (both perfect and partition), less than the less risk averse one. On the other hand, if both decision makers initially accept the investment, or are indifferent to the investment without the information, then (i) the more risk-averse decision maker will value perfect information higher than the less risk-averse one, but (ii) this monotonicity result need not apply for the case of partition information. These results enable us to compare the value of information when decision makers have different risk aversion levels. They also hold when comparison of risk aversion is restricted only to a domain defined by the lottery.

Risk Preferences

Risk attitudes include risk aversion as well as higher-order risk preferences such as prudence and temperance. This article analyzes the effects of such preferences on medical test and treatment decisions, represented either by test and treatment thresholds or-when the test result is not given-by optimal cutoff values for diagnostic tests. For a risk-averse decision maker, effective treatment is a risk-reducing strategy since it prevents the low health outcome of forgoing treatment in the sick state. Compared with risk neutrality, risk aversion thus lowers both the test and the treatment threshold and decreases the optimal test cutoff value. Risk vulnerability, which combines risk aversion, prudence, and temperance, is relevant if there is a comorbidity risk: thresholds and optimal cutoff values decrease even more. Since common utility functions imply risk vulnerability, our findings suggest that diagnostics in low prevalence settings (e.g., screening) may be considered more beneficial when risk preferences are taken into account.

Serotonin 2A receptors contribute to the regulation of risk-averse decisions

Pharmacological studies point to a role of the neurotransmitter serotonin (5-HT) in regulating the preference for risky decisions, yet the functional contribution of specific 5-HT receptors remains to be clarified. We used pharmacological fMRI to investigate the role of the 5-HT2A receptors in processing negative outcomes and regulating risk-averse behavior. During fMRI, twenty healthy volunteers performed a gambling task under two conditions: with or without blocking the 5-HT2A receptors. The volunteers repeatedly chose between small, likely rewards and large, unlikely rewards. Choices were balanced in terms of expected utility and potential loss. Acute blockade of the 5-HT2A receptors with ketanserin made participants more risk-averse. Ketanserin selectively reduced the neural response of the frontopolar cortex to negative outcomes that were caused by low-risk choices and were associated with large missed rewards. In the context of normal 5-HT2A receptor function, ventral striatum displayed a stronger response to low-risk negative outcomes in risk-taking as opposed to risk-averse individuals. This (negative) correlation between the striatal response to low-risk negative outcomes and risk-averse choice behavior was abolished by 5-HT2A receptor blockade. The results provide the first evidence for a critical role of 5-HT2A receptor function in regulating risk-averse behavior. We suggest that the 5-HT2A receptor system facilitates risk-taking behavior by modulating the outcome evaluation of “missed” reward. These results have implications for understanding the neural basis of abnormal risk-taking behavior, for instance in pathological gamblers.

Aviation Security, Risk Assessment, and Risk Aversion for Public Decisionmaking

This paper estimates risk reductions for each layer of security designed to prevent commercial passenger airliners from being commandeered by terrorists, kept under control for some time, and then crashed into specific targets. Probabilistic methods are used to characterize the uncertainty of rates of deterrence, detection, and disruption, as well as losses. Since homeland security decisionmakers tend to be risk-averse because of the catastrophic or dire nature of the hazard or event, utility theory and Monte Carlo simulation methods are used to propagate uncertainties in calculations of net present value, expected utility, and probabilities of net benefit. We employ a “break-even” cost-benefit analysis to determine the minimum probability of an otherwise successful attack that is required for the benefit of security measures to equal their cost. In this context, we examine specific policy options: including Improvised Physical Secondary Barriers (IPSBs) in the array of aircraft security measures, including the Federal Air Marshal Service (FAMS), and including them both. Attack probabilities need to exceed 260 percent or 2.6 attacks per year to be 90 percent sure that FAMS is cost-effective, whereas IPSBs have more than 90 percent chance of being cost-effective even if attack probabilities are as low as 6 percent per year. A risk-neutral analysis finds a policy option of adding IPSBs but not FAMS to the other measures to be preferred for all attack probabilities. However, a very risk-averse decisionmaker is 48 percent likely to prefer to retain FAMS even if the attack probability is as low as 1 percent per year—a level of risk aversion exhibited by few, if any, government agencies. Overall, it seems that, even in an analysis that biases the consideration toward the opposite conclusion, far too much may currently be spent on security measures to address the problem of airline hijacking, and many spending reductions could likely be made with little or no consequent reduction of security.

I can take the risk, but you should be safe: Self-other differences in situations involving physical safety

AbstractPrior research on self-other differences involving risk have found that individuals make riskier decisions for others than for the self in situations where risk taking is valued. We expand this research by examining whether the direction of self-other differences reverses when risk aversion is valued, as predicted by social values theory (Stone & Allgaier, 2008). Two studies tested for self-other differences in physical safety scenarios, a domain where risk aversion is valued. In Study 1, participants read physical safety and romantic relationship scenarios and selected what they would decide for themselves, what they would decide for a friend, or what they would predict their friend would decide. In Study 2, participants read public health scenarios and either decided or predicted for themselves and for a friend. In keeping with social values theory, participants made more risk-averse decisions for others than for themselves in situations where risk aversion is valued (physical safety scenarios) but more risk-taking decisions for others than for themselves in situations where risk taking is valued (relationship scenarios). Further, we show that these self-other differences in decision making do not arise from incorrectly predicting others’ behaviors, as participants predicted that others’ decisions regarding physical safety scenarios would be either similar (Experiment 1) or more risktaking(Experiment 2) than their own decisions.

Decision tree analysis for a risk averse decision maker: CVaR Criterion

Risk aversion is a prevalent phenomenon when sufficiently large amounts are at risk. In this paper, we introduce a new prescriptive approach for coping with risk in sequential decision problems with discrete scenario space. We use Conditional Value-at-Risk (CVaR) risk measure as optimization criterion and prove that there is an explicit linear representation of the proposed model for the problem.

Ability of Matrix Models to Explain the Past and Predict the Future of Plant Populations

Uncertainty associated with ecological forecasts has long been recognized, but forecast accuracy is rarely quantified. We evaluated how well data on 82 populations of 20 species of plants spanning 3 continents explained and predicted plant population dynamics. We parameterized stage-based matrix models with demographic data from individually marked plants and determined how well these models forecast population sizes observed at least 5 years into the future. Simple demographic models forecasted population dynamics poorly; only 40% of observed population sizes fell within our forecasts' 95% confidence limits. However, these models explained population dynamics during the years in which data were collected; observed changes in population size during the data-collection period were strongly positively correlated with population growth rate. Thus, these models are at least a sound way to quantify population status. Poor forecasts were not associated with the number of individual plants or years of data. We tested whether vital rates were density dependent and found both positive and negative density dependence. However, density dependence was not associated with forecast error. Forecast error was significantly associated with environmental differences between the data collection and forecast periods. To forecast population fates, more detailed models, such as those that project how environments are likely to change and how these changes will affect population dynamics, may be needed. Such detailed models are not always feasible. Thus, it may be wiser to make risk-averse decisions than to expect precise forecasts from models.