RISK AVERSION,WEALTH, AND BACKGROUND RISK

We use household survey data to construct a direct measure of absolute risk aversion based on the maximum price a consumer is willing to pay for a risky security. We relate this measure to consumer's endowments and attributes and to measures of background risk and liquidity constraints. We find that risk aversion is a decreasing function of the endowment—thus rejecting CARA preferences. We estimate the elasticity of risk aversion to consumption at about 0.7, below the unitary value predicted by CRRA utility. We also find that households' attributes are of little help in predicting their degree of risk aversion, which is characterized by massive unexplained heterogeneity. We show that the consumer's environment affects risk aversion. Individuals who are more likely to face income uncertainty or to become liquidity constrained exhibit a higher degree of absolute risk aversion, consistent with recent theories of attitudes toward risk in the presence of uninsurable risks. (JEL: D1, D8)     

The Law of Demand and Risk Aversion

This note proposes a necessary and sufficient condition on a utility function to guarantee that it generates a demand function satisfying the law of demand. This condition can be interpreted in terms of an agent's attitude towards lotteries in commodity space. As an application, we show that when an agent has an expected utility function, her demand for securities satisfies the law of demand if her coefficient of relative risk aversion does not vary by more than 4.     

可加效用下基于消费者惰性的易逝品动态定价

本文在考虑销售商的风险规避态度和消费者惰性的情况下，研究了易逝品的动态定价策略。首先给出风险规避的销售商实施动态定价的马尔可夫决策过程，并运用MNL随机效用模型来刻画惰性消费者的购买决策，在此基础上，以风险规避销售商的期望效用最大化为目标，利用动态规划方法建立了可加效用下的易逝品动态定价模型，并探讨了消费者的惰性行为和销售商的风险规避态度对最优价格的影响。结论表明：在销售商的风险态度为风险规避的情况下，考虑消费者惰性行为的最优价格随库存水平的增加而降低，随剩余销售时间的增加而提高，消费者的惰性行为和销售商的风险规避态度对最优价格都存在负向影响，即最优价格随惰性深度的增加而降低，随惰性宽度的增加而降低，同时，销售商的风险规避态度越强烈，其制定的产品价格越低。     

Calibration Results for Non‐Expected Utility Theories

Rabin (2000) proved that a low level of risk aversion with respect to small gambles leads to a high, and absurd, level of risk aversion with respect to large gambles. Rabin's arguments strongly depend on expected utility theory, but we show that similar arguments apply to general non‐expected utility theories.     

Workers’ Risk Tolerance and Occupational Injuries

This study explores the relationship between individuals’ risk tolerance and occupational injuries. We analyze data from a national representative survey of U.S. workers that includes information about injuries, risk tolerance, cognitive and noncognitive attributes, and risky behaviors. We measure risk tolerance through questions regarding individuals’ willingness to gamble on their lifetime income. We estimate zero‐inflated count models to assess the role played by such measures on workers’ recurrent injuries. We discuss some implications of our results for future research and occupational safety policies. Our results highlight the concurrent and changing role played by individual, work, and environmental factors in explaining recurrent incidents. They show that risk tolerance affects recurrent injuries, although not in the direction that proponents of the concept of proneness would expect. Our measure of risk aversion shows that individuals who are somewhat more risk tolerant have fewer recurrent injuries than those who are risk averse. But the estimated relationship is U‐shaped, not monotonic and, therefore, not easy to predict. At the same time, we find that individuals’ “revealed risk preferences”—specific risky behaviors—are related to higher injury probabilities. Demanding working conditions, measures of socioeconomic status, health, and safety problems experienced by workers during their youth remain among the most important factors explaining the phenomena of recurrent injuries. So our results contribute also to the important debate about the relationship between health and socioeconomic status.     

Flood Risk,Flood Mitigation,and Location Choice: Evaluating the National Flood Insurance Program's Community Rating System

Climate change is expected to worsen the negative effects of natural disasters like floods. The negative impacts, however, can be mitigated by individuals’ adjustments through migration and relocation behaviors. Previous literature has identified flood risk as one significant driver in relocation decisions, but no prior study examines the effect of the National Flood Insurance Program's voluntary program—the Community Rating System (CRS)—on residential location choice. This article fills this gap and tests the hypothesis that flood risk and the CRS‐creditable flood control activities affect residential location choices. We employ a two‐stage sorting model to empirically estimate the effects. In the first stage, individuals’ risk perception and preference heterogeneity for the CRS activities are considered, while mean effects of flood risk and the CRS activities are estimated in the second stage. We then estimate heterogeneous marginal willingness to pay (WTP) for the CRS activities by category. Results show that age, ethnicity and race, educational attainment, and prior exposure to risk explain risk perception. We find significant values for the CRS‐creditable mitigation activities, which provides empirical evidence for the benefits associated with the program. The marginal WTP for an additional credit point earned for public information activities, including hazard disclosure, is found to be the highest. Results also suggest that water amenities dominate flood risk. Thus, high amenity values may increase exposure to flood risk, and flood mitigation projects should be strategized in coastal regions accordingly.     

APPLICATIONS OF A RISK AVERSION CONCEPT

In decision theory the concept denoted variously as “risk aversion increment” or “risk premium” has not been fully exploited, although it is neither new nor complex. In this paper we will show how the concept of the risk aversion increment can be used for developing an alternative to the explicit use of the utility function. For most people the use of a risk aversion increment provides a better conceptual reference than does the use of a utility function. To illustrate the usefulness of the concept as a basis for gaining insight into problem statements and their analysis, the following applications are developed: 1) general results for the exponential utility function. 2) estimation of utility functions. 3) general results for various combinations of utility functions and probability distributions. 4) use in sequential decisions. 5) application in the theory of incentives.     

定价核之谜与概率权重函数

采用期权及标的资产价格数据, 基于离散时间EGARCH模型和连续时间GARCH扩散模型分别估计了客观与风险中性密度, 进而推导了经验定价核. 在此基础上, 基于等级依赖期望效用模型, 在标准的效应函数形式下构建了相应的概率权重函数. 采用香港恒生指数及其指数权证价格数据进行实证研究, 结果表明: (1) 经验定价核不是单调递减的, 而是展现出驼峰(非单调性), 即“定价核之谜”;(2) 经验概率权重函数展现S型, 表明市场投资者低估尾部概率事件, 高估中、高概率事件;(3) “定价核之谜”可以由具有标准效用函数与S型概率权重函数的等级依赖期望效用模型解释。     

Is time consistency compatible with risk aversion?

Managerial decision models applied in operations research, finance, information management, and many other disciplines are typically both dynamic and stochastic. When decisions at different points in time are allowed, the question arises what conditions guarantee the absence of incentives to deviate from the ex ante optimal policy at later dates. We term such a policy time consistent. A well-known result states that additively separable objective functions ensure time consistency under risk neutrality. Unfortunately, this is no longer true when decision makers are risk averse. Then, (much) more restrictive assumptions are needed. The aim of this paper is to provide clear-cut conditions that ensure time consistency in an expected utility framework. Our main findings are twofold: on the one hand, constant absolute risk aversion can guarantee time consistency when final values are under consideration. On the other hand, time consistency and risk aversion are incompatible when intertemporal payments are aggregated by means of net present values.     

基于动态损失厌恶投资组合模型的最优资产配置与实证研究

从行为金融学的角度考虑投资者损失厌恶的心理特征,建立预期效用最大化的动态损失厌恶投资组合优化模型。以我国股票市场为依托,将市场分为上升、下降和盘整三种状态,研究动态损失厌恶投资组合模型的最优资产配置和绩效表现,并与静态损失厌恶投资组合模型、M-V投资组合模型和CVaR投资组合模型进行比较。最后,在具有交易成本的条件下对动态模型进行稳健性检验。得出结论：不同情况下,动态损失厌恶投资者具有不同的最优资产配置比例,且动态损失厌恶投资组合模型明显优于静态模型、M-V投资组合模型和CVaR投资组合模型。     

Measurement error, skewness, and risk analysis: coping with the long tail of the distribution.

Probabilistic risk analyses often construct multistage chance trees to estimate the joint probability of compound events. If random measurement error is associated with some or all of the estimates, we show that resulting estimates of joint probability may be highly skewed. Joint probability estimates based on the analysis of multistage chance trees are more likely than not to be below the true probability of adverse events, but will sometimes substantially overestimate them. In contexts such as insurance markets for environmental risks, skewed distributions of risk estimates amplify the "winner's curse" so that the estimated risk premium for low-probability events is likely to be lower than the normative value. Skewness may result even in unbiased estimators of expected value from simple lotteries, if measurement error is associated with both the probability and pay-off terms. Further, skewness may occur even if the error associated with these two estimates is symmetrically distributed. Under certain circumstances, skewed estimates of expected value may result in risk-neutral decisionmakers exhibiting a tendency to choose a certainty equivalent over a lottery of equal expected value, or vice versa. We show that when distributions of estimates of expected value are, positively skewed, under certain circumstances it will be optimal to choose lotteries with nominal values lower than the value of apparently superior certainty equivalents. Extending the previous work of Goodman (1960), we provide an exact formula for the skewness of products.     

Promoting Seismic Retrofit Implementation Through “Nudge”: Using Warranty as a Driver

This article proposes a new type of warranty policy that applies the “nudge” concept developed by Thaler and Sunstein to encourage homeowners in Japan to implement seismic retrofitting. Homeowner adaptation to natural disasters through loss reduction measures is known to be inadequate. To encourage proactive risk management, the “nudge” approach capitalizes on how choice architecture can influence human decision‐making tendencies. For example, people tend to place more value on a warranty for consumer goods than on actuarial value. This article proposes a “warranty for seismic retrofitting” as a “nudge” policy that gives homeowners the incentive to adopt loss reduction measures. Under such a contract, the government guarantees all repair costs in the event of earthquake damage to the house if the homeowner implements seismic retrofitting. To estimate the degree to which a warranty will increase the perceived value of seismic retrofitting, we use field survey data from 1,200 homeowners. Our results show that a warranty increases the perceived value of seismic retrofitting by an average of 33%, and an approximate cost‐benefit analysis indicates that such a warranty can be more economically efficient than an ex ante subsidy. Furthermore, we address the failure of the standard expected utility model to explain homeowners’ decisions based on warranty evaluation, and explore the significant influence of ambiguity aversion on the efficacy of seismic retrofitting and nonanalytical factors such as feelings or trust.     

Savage in the Market

We develop a behavioral axiomatic characterization of subjective expected utility (SEU) under risk aversion. Given is an individual agent's behavior in the market: assume a finite collection of asset purchases with corresponding prices. We show that such behavior satisfies a “revealed preference axiom” if and only if there exists a SEU model (a subjective probability over states and a concave utility function over money) that accounts for the given asset purchases.     

The Effect of Changes in Risk Attitude on Strategic Behavior

We study families of normal‐form games with fixed preferences over pure action profiles but varied preferences over lotteries. That is, we subject players' utilities to monotone but nonlinear transformations and examine changes in the rationalizable set and set of equilibria. Among our results: The rationalizable set always grows under concave transformations (risk aversion) and shrinks under convex transformations (risk love). The rationalizable set reaches an upper bound under extreme risk aversion, and lower bound under risk love, and both of these bounds are characterized by elimination processes. For generic two‐player games, under extreme risk love or aversion, all Nash equilibria are close to pure and the limiting set of equilibria can be described using preferences over pure action profiles.     

动态均值-方差资产组合的有效性:时变风险容忍度视角

尽管均值-方差模型在静态资产组合优化过程中得到广泛运用并证明是有效的,但在动态情景下,均值-方差模型运用于动态资产组合优化过程中的有效性问题引起人们的质疑：一是常风险规避系数的设定不符合事实;二是投资者偏好设定不符合动态情景下的主流效用函数族。鉴于此,本文假设投资者风险容忍度是资产组合投资期与投资者期望收益率的函数,研究动态均值-方差资产组合的有效性问题。基于均值-方差分析框架构建时变风险容忍度下的动态资产组合模型;运用伊藤定理和拉格朗日乘子法获得最优资产组合封闭解;基于二次效用偏好下的动态资产组合,从资产组合策略、夏普率、确定性等价收益率和有效前沿等视角验证动态均值-方差资产组合策略和业绩,并予以实证。结果表明：动态均值-方差资产组合不但具有同等业绩而且体现了其灵活性和风险对冲价值;尽管动态均值-方差资产组合表现出高杠杆性,但其确定性等价收益率较高,且随投资期的增加呈现倒U型趋势;动态均值-方差资产组合的投资期效应显著,强于投资者期望收益率。研究指出,时变风险容忍度下的动态均值-方差资产组合管理和优化策略有效,但在短投资期（低于12个月）和（或）低期望收益率下并不适用。研究不但拓展了均值-方差模型在动态情境下的应用,而且体现了投资者源于心理和（或）其财富变化的投资行为调整。     

Measuring Inequity Aversion in a Heterogeneous Population Using Experimental Decisions and Subjective Probabilities

We combine choice data in the ultimatum game with the expectations of proposers elicited by subjective probability questions to estimate a structural model of decision making under uncertainty. The model, estimated using a large representative sample of subjects from the Dutch population, allows both nonlinear preferences for equity and expectations to vary across socioeconomic groups. Our results indicate that inequity aversion to one's own disadvantage is an increasing and concave function of the payoff difference. We also find considerable heterogeneity in the population. Young and highly educated subjects have lower aversion for inequity than other groups. Moreover, the model that uses subjective data on expectations generates much better in‐ and out‐of‐sample predictions than a model which assumes that players have rational expectations.     

Dispositional Factors Affecting Choices Surrounding the Purchase of Insurance and the Taking of Mitigating Measures Against Flooding

This research investigated the role of dispositional factors in decisions to purchase insurance and to take mitigating measures against flooding. Two dispositional factors—risk aversion in the domain of losses and time discounting rate—were found to be predictors of the decision to acquire flood insurance. The observation of a relationship between experiment-based risk attitudes and the decision to insure oneself against flooding replicates a finding of Petrolia et al. The finding that impatience negatively impacts decisions to take out insurance against flooding is novel. However, support was not found for analogous hypotheses concerning relationships between the two dispositional variables and decisions to take mitigating measures. Evidently, factors other than individual risk aversion and time discounting rate play a crucial role in this behavior.     

不同权力结构和联盟策略下风险规避型闭环供应链决策

本文旨在探讨不同渠道权力结构和联盟策略下风险规避型闭环供应链的决策问题。考虑到产品需求和废旧产品回收的不确定性及决策者的风险规避特性,在制造商主导、零售商主导及制造商和零售商势力均衡三种情形下,分别构建了制造商和零售商联盟与不联盟时的闭环供应链博弈模型,获得了六个博弈模型下的均衡解,对比分析了不同模型下产品定价、废旧产品的最优回收价格和供应链及其成员的期望收益。研究结果表明,在制造商和零售商不联盟的情形下,决策者的风险规避程度增加能够缓解双重边际效应,供应链期望收益与风险规避程度正相关,而在制造商和零售商联盟的情形下,供应链期望收益与风险规避程度负相关;制造商和零售商不联盟时,制造商和零售商势力均衡的渠道权力结构对消费者最有利,而制造商和零售商联盟时,制造商和零售商势力均衡的渠道权力结构对消费者最不利;制造商和零售商权力结构不对等时最优价格决策之间的关系与制造商和零售商的风险规避程度有关;供应链期望收益在制造商和零售商势力均衡下最大,制造商期望收益在制造商主导的渠道权力结构下最大,零售商期望收益在零售商主导的渠道权力结构下最大。     

基于ART及多风险规避的交通网络均衡模型

随着对交通系统不确定性认识的深入,以绝对理性为基础的“期望效用理论”在风险环境下的路径选择分析中显示出局限性,而“预期后悔理论”则为之提供了新的分析思路.将预期后悔理论应用到风险环境下的路径选择分析中,将出行者一致风险规避的假设扩展到多风险规避,建立了基于后悔理论及多风险规避出行特征的交通网络随机用户均衡变分不等式模型,并给出了求解算法.通过算例分析发现,后悔心理对出行者的路径选择并不总是显著的.在非风险环境及极端风险环境中,后悔心理对出行者的路径选择影响是微弱的,但是当环境处于极端风险与非风险之间时,后悔心理对出行者路径选择有着较为显著的影响.     

Random Expected Utility

We develop and analyze a model of random choice and random expected utility. A decision problem is a finite set of lotteries that describe the feasible choices. A random choice rule associates with each decision problem a probability measure over choices. A random utility function is a probability measure over von Neumann–Morgenstern utility functions. We show that a random choice rule maximizes some random utility function if and only if it is mixture continuous, monotone (the probability that a lottery is chosen does not increase when other lotteries are added to the decision problem), extreme (lotteries that are not extreme points of the decision problem are chosen with probability 0), and linear (satisfies the independence axiom).