Showing papers on "Ambiguity aversion published in 2003"
TL;DR: In this article, the authors propose a model of preferences over acts such that the decision maker evaluates acts according to the expectation (over a set of probability measures) of an increasing transformation of an act's expected utility.
Abstract: We propose and axiomatize a model of preferences over acts such that the decision maker evaluates acts according to the expectation (over a set of probability measures) of an increasing transformation of an act's expected utility. This expectation is calculated using a subjective probability over the set of probability measures that the decision maker thinks are relevant given her subjective information. A key feature of our model is that it achieves a separation between ambiguity, identified as a characteristic of the decision maker's subjective information, and ambiguity attitude, a characteristic of the decision maker's tastes. We show that attitudes towards risk are characterized by the shape of the von Neumann-Morgenstern utility function, as usual, while attitudes towards ambiguity are characterized by the shape of the increasing transformation applied to expected utilities. We show that the negative exponential form of this transformation is the special case of constant ambiguity aversion. Ambiguity itself is defined behaviorally and is shown to be characterized by properties of the subjective set of measures. This characterization of ambiguity is formally related to the definitions of subjective ambiguity advanced by Epstein-Zhang (2001) and Ghirardato-Marinacci (2002). One advantage of this model is that the well-developed machinery for dealing with risk attitudes can be applied as well to ambiguity attitudes. The model is also distinct from many in the literature on ambiguity in that it allows smooth, rather than kinked, indifference curves. This leads to different behavior and improved tractability, while still sharing the main features (e.g., Ellsberg's Paradox, etc.). The Maxmin EU model (e.g., Gilboa and Schmeidler (1989)) with a given set of measures may be seen as an extreme case of our model with infinite ambiguity aversion. Two illustrative applications to portfolio choice are offered.
1,475 citations
TL;DR: A methodology based on multiple criteria mathematical programming to obtain relative and absolute risk aversion coefficients is presented, which relies on multiattribute utility theory to elicit a separable additive multi attribute utility function and estimate the risk aversion coefficient.
135 citations
TL;DR: In this article, the authors investigated how decision makers respond to ambiguous information about costs and benefits and found that decision makers discount ambiguous information, which is related to insights on the disjunction effect, the sunk cost effect, transaction decoupling, and ambiguity aversion.
Abstract: In three experimental studies we investigated how decision makers respond to ambiguous information about costs and benefits. In Experiment 1, we studied the effect of ambiguity about prior costs. Experiments 2 and 3 focused on the effect of ambiguity about future outcomes. The collective results of the three studies suggest that decision makers discount ambiguous information. The findings are related to insights on the disjunction effect, the sunk cost effect, transaction decoupling, and ambiguity aversion. Copyright # 2003 John Wiley & Sons, Ltd.
117 citations
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TL;DR: In this article, a large sample of individual responses to six lottery questions is analyzed and a simultaneous estimate of risk aversion and the time preference discount rate per individual is derived, where the consumption of a large prize is smoothed over a larger time period.
Abstract: In this paper we analyze a large sample of individual responses to six lottery questions. We derive a simultaneous estimate of risk aversion and the time preference discount rate per individual. This can be done because the consumption of a large prize is smoothed over a larger time period. It is found that both parameters strongly vary over individuals, while they are moderately negatively correlated. Furthermore we explain the estimated relative risk aversion and time preference by income, age, gender, entrepreneurship and an obesity index. Very significant effects are found. If we explain relative risk aversion in a simple model where time discounting is ignored, we find completely different estimates for this parameter. We conclude that in the case of lotteries with big prizes a simultaneous estimate of risk aversion and time preference is needed in order to avoid misspecification
106 citations
TL;DR: This article examined the joint influence of uncertain delay and risk in an original sample of business owners and managers and found that many subjects disliked uncertainty in the timing of an outcome, a reaction they termed "lottery timing risk aversion." Such aversion to uncertain timing was positively related to aversion to ambiguous probability abilities for lotteries involving storm damage risks.
Abstract: Optimal protective responses to long-term risks depend on rational perceptions of ambiguous risks and uncertain time horizons. Our study examined the joint influence of uncertain delay and risk in an original sample of business owners and managers. We found that many subjects disliked uncertainty in the timing of an outcome, a reaction we term "lottery timing risk aversion." Such aversionto uncertain timing was positivelyrelated to aversion to ambiguousprob- abilities for lotteries involving storm damage risks. This association suggests that uncertainty may be processed similarly in both the risk and time dimensions. Timeand uncertainty complicate many choices we make. Numerous studies have suggested that there are forms of irrationality that arise in both the time and risk dimension and that people perceive future outcomes and uncertain outcomes in a cognitively similar manner. 1 That is, an agent's information processing in situations involving risk is closely related to the agent's processing of information re- garding future outcomes. The existence of such parallels suggests that the same anomalies influencing how subjects process uncertain risks may determine the processing of uncertainty in the timing of an outcome. This paper examines the preferences that many people have for certainty in the timing of an outcome, a preference which we call "lottery timing risk aversion." Uncertainty regarding the timing of a payoff leads to behavior which would not likely be predicted by expected utility theory. 2 In addition to documenting this phenomenon, we specifically link aversion to uncertainty in the time dimension to the ambiguity aversion reflected in the Ells- berg Paradox for probabilities at a point in time. 3 More specifically, ∗ The U.S. Government's right to retain a non-exclusive, royalty-free licence
73 citations
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TL;DR: In this paper, the authors present methodology and a laboratory experiment, which separates inequality aversion from risk aversion, in a set of laboratory experiments, subjects had to choose between two risky alternatives which pay meaningful prizes with the same individual risk but different levels of egalitarianism.
Abstract: Inequality aversion and risk-aversion are widely assumed in economic models; however existing economic literature fails to distinguish between the two. This paper presents methodology and a laboratory experiment, which separates inequality aversion from risk aversion. In a set of laboratory experiments, subjects had to choose between two risky alternatives which pay meaningful prizes with the same individual risk but different levels of egalitarianism. Thus, the choice of the more egalitarian alternative implies a higher level of inequality aversion. The experiment was conducted among children, some of whom live on a communal system (kibbutz) and some in the city.
65 citations
TL;DR: This paper found that if the task is perceived as cooperative (a partner or friend is composing the boxes) people are indifferent toward ambiguity or even ambiguity seeking, while people expect their winning odds to be less than even in the ambiguous box.
Abstract: Ambiguity avoidance denotes people's preference for gambling situations with known over unknown, or ambiguous, probability distributions. In four experiments we provide evidence for the interaction between competitiveness and knowledge in Ellsberg's task, in which people have a choice between a risky box (distribution of balls known) and an ambiguous box (distribution of balls not known). If the situation is perceived as competitive (the experimenter or an opponent is responsible for composing the boxes) people avoid ambiguity by betting on the box with the known probability distribution. If the task is perceived as cooperative (a partner or friend is composing the boxes) people are indifferent toward ambiguity or even ambiguity seeking. In addition, we find that people expect their winning odds to be less than even in the ambiguous box. Copyright © 2003 John Wiley & Sons, Ltd.
44 citations
TL;DR: In this article, the authors characterize comparative mixed risk aversion so as to answer the following question: how different risk attitudes affect choices when expenditures change event probabilities? Attempts to answer this question in the literature found an endogenous probability.
Abstract: Mixed risk aversion (Caballe and Pomansky, 1996) defines the class of increasing utility functions that have derivatives alternating in sign, with positive odd derivatives and negative even derivatives. In this article, we characterize comparative mixed risk aversion so as to answer the following question: how different risk attitudes affect choices when expenditures change event probabilities? Attempts to answer this question in the literature found an endogenous probability. We show that the threshold probability is 1/2 under mixed risk aversion. We consider applications to self-protection and willingness to pay. We obtain that if agent v is more mixed risk averse than agent u, then v will select a higher level of self-protection and will have a higher willingness to pay than u only if the accident probability is lower than 1/2. We extend the results to the presence of a background risk.
43 citations
TL;DR: The Pratt-Arrow measure of local risk aversion is generalized for then-dimensional state-preference model of choice under uncertainty in which the decision maker may have inseparable subjective probabilities and utilities, unobservable stochastic prior wealth, and/or smooth nonexpected-utility preferences.
Abstract: The Pratt-Arrow measure of local risk aversion is generalized for then-dimensional state-preference model of choice under uncertainty in which the decision maker may have inseparable subjective probabilities and utilities, unobservable stochastic prior wealth, and/or smooth nonexpected-utility preferences. Local risk aversion is measured by the matrix of derivatives of the decision maker's risk-neutral probabilities, without reference to true subjective probabilities or riskless wealth positions, and comparative risk aversion is measured without requiring agreement on true probabilities. Risk-neutral probabilities and their derivatives are shown to be sufficient statistics for approximately optimal investment and financing decisions in complete markets for contingent claims.
39 citations
TL;DR: In this article, the authors extend the real options approach to incorporate risk aversion for a general class of utility functions and show that risk aversion provides an incentive for the investor to delay investment and leads to a significant erosion in project values.
Abstract: In the standard real options approach to investment under uncertainty, agents formulate optimal policies under the assumptions of risk neutrality or complete financial markets. Although these assumptions are crucial to the implications of the approach, they are not particularly relevant to most real-world environments where agents face incomplete markets and are exposed to undiversifiable risks. In this paper we extend the real options approach to incorporate risk aversion for a general class of utility functions. We show that risk aversion provides an incentive for the investor to delay investment and leads to a significant erosion in project values.
35 citations
01 Jan 2003
TL;DR: The model-based multiple-priors theory as discussed by the authors generalizes existing theories of dynamic choice under uncertainty aversion by relaxing the assumption of consequentialism, which can be problematic when combined with uncertainty aversion.
Abstract: Most asset returns are uncertain, not merely risky: investors do not know the probabilities of dieren t possible future returns. A large body of evidence suggests that investors are averse to uncertainty, as well as to risk. This paper builds up an axiomatic foundation for the dynamic portfolio and consumption choices of an uncertainty-averse (as well as risk-averse) investor who tries to learn from historical data. The theory developed, model-based multiplepriors, generalizes existing theories of dynamic choice under uncertainty aversion by relaxing the assumption of consequentialism. Examples are given to show that consequentialism, the property that counterfactuals are ignored, can be problematic when combined with uncertainty aversion. An analog of de Finetti’s statistical representation theorem is proven under model-based multiple-priors, but consequentialism combines with multiple priors to rule out prior-by-prior exchangeability. A simple dynamic portfolio choice problem illustrates the contrast between a model-based multiple-priors investor and a consequentialist multiple-priors investor.
TL;DR: The authors found that when faced with a decision how to split their investment between a risky lottery and an asset with a fixed return, people increase the proportion invested in the risky option the more they like the lottery.
Abstract: We study the following basic intuition: when faced with a decision how to split their investment between a risky lottery and an asset with a fixed return, people increase the proportion invested in the risky option the more they like the lottery. We find counter-examples to this, and in fact we find no simple relation between preferences between lotteries and the fraction invested in them. We use three well-documented biases (ambiguity aversion, the illusion of control and myopic loss aversion) to show this. First we replicate the previous results in a laboratory experiment with financial incentives, and then test whether participants are willing to explicitly pay a small sum of money in line with the bias (pay for less ambiguity, more perceived control, or more frequent information about portfolio performance). We then study how portfolio choice depends on these biases. With the parameters chosen, the illusion of control was eliminated when participants were asked to pay to gain more control, and the bias did not affect investment behavior (i.e., participants invested in a risky option the same fraction when faced with more or less control). In the ambiguity treatment, people were willing to pay for less ambiguity, but again the level of ambiguity did not influence investment. Finally, in the myopic loss aversion treatment participants were willing to pay money to have more freedom to choose, even though (in line with the documented bias) they invested less when having more freedom to change their investment.
TL;DR: In this paper, rank-dependent utility theory is used to model bargaining problems, where the preferences of the bargainers deviate from expected utility but can be modelled according to rank dependent utility theory.
TL;DR: In this article, a connection between portfolio inertia and ambiguity is established without invoking a parametric preference form, such as the Choquet expected utility or the max-min multiple priors model.
01 Jan 2003
TL;DR: In this paper, the authors discuss the formal definition of ambiguity and ambiguity attitude, showing that it is represented mathematically by the convexity of the decision maker's capacity v. (1/2)f+ ∗Dipartimento di Matematica Applicata and ICER, Universita di Torino.
Abstract: According to the well-known distinction attributed to Knight (1921), there are two kinds of uncertainty. The first, called “risk,” corresponds to situations in which all events relevant to decision making are associated with obvious probability assignments (which every decision maker agrees to). The second, called “(Knightian) uncertainty” or (following Ellsberg (1961)) “ambiguity,” corresponds to situations in which some events do not have an obvious, unanimously agreeable, probability assignment. As Chapter 1 makes clear, this collection focuses on the issues related to decision making under ambiguity. In this Chapter, I briefly discuss the issue of the formal definition of ambiguity and ambiguity attitude. In his seminal paper on the CEU model (1989), Schmeidler proposed a behavioral definition of ambiguity aversion, showing that it is represented mathematically by the convexity of the decision maker’s capacity v. The property he proposed can be understood by means of the example of the two coins used in Chapter 1. Assume that the decision maker places bets that depend on the result of two coin flips, the first of a coin that she is very familiar with, the second of a coin provided by somebody else. Given that she is not familiar with the second coin, it is possible that she would consider“ambiguous” all the bets whose payoff depends on the result of the second flip. (For instance, a bet that pays $1 if the second coin lands with heads up, or equivalently if the event {HH, TH} obtains.) If she is averse to ambiguity, she may therefore see such bets as somewhat less desirable that bets that are “unambiguous,” i.e., only depend on the result of the first flip. (For instance, a bet that pays $1 if the first coin lands with heads up, or equivalently if the event {HH, HT} obtains.) However, suppose that we give the decision maker the possibility of buying shares of each bet. Then, if she is offered a bet that pays $0.50 on {HH} and $0.50 on {HT}, she may prefer it to either of the two ambiguous bets. In fact, such a bet has the same contingent payoffs as a bet which pays $0.50 if the first coin lands with heads up, which is unambiguous. That is, a decision maker who is averse to ambiguity may prefer the equal-probability “mixture” of two ambiguous acts to either of the acts. In contrast, a decision maker who is attracted to ambiguity may prefer to choose one of the ambiguous acts. Formally, Schmeidler called ambiguity averse a decision maker who prefers the even mixture1 (1/2)f+(1/2)g of two acts that she finds indifferent to either of the two acts. That is, (1/2)f+ ∗Dipartimento di Matematica Applicata and ICER, Universita di Torino. Recall that Schmeidler used the Anscombe-Aumann setting, in which mixtures of acts can be defined stateby-state. Also, he used the term “uncertainty” averse rather than ambiguity averse.
TL;DR: This article characterizes attitudes to uncertainty by means of no Dutch books conditions, and excludes Dutch books on more reduced sets, which is equivalent to having concave or convex Choquet integrals.
TL;DR: In this article, the authors define decreasing absolute risk aversion in purely behavioral terms without any assumption of differentiability and show that a strictly increasing and risk averse utility function with decreasing absolute aversion is necessarily differentiable with an absolutely continuous derivative.
Abstract: This paper defines decreasing absolute risk aversion in purely behavioral terms without any assumption of differentiability and shows that a strictly increasing and risk averse utility function with decreasing absolute risk aversion is necessarily differentiable with an absolutely continuous derivative. A risk averse utility function has decreasing absolute risk aversion if and only if it has a decreasing absolute risk aversion density, and if and only if the cumulative absolute risk aversion function is increasing and concave. This leads to a characterization of all such utility functions. Analogues of these results also hold for increasing absolute and for increasing and decreasing relative risk aversion.
TL;DR: In this paper, the authors generalize the theory of irreversible investment under uncertainty by allowing for risk averse investors in the absence of complete markets, and show that risk aversion reduces investment, particularly if the investment size is large.
Abstract: This paper generalizes the theory of irreversible investment under uncertainty by allowing for risk averse investors in the absence of com-plete markets.Until now this theory has only been developed in the cases of risk neutrality, or risk aversion in combination with complete markets.Within a general setting, we prove the existence of a unique critical output price that distinguishes price regions in which it is optimal for a risk averse investor to invest and price regions in which one should refrain from investing.We use a class of utility functions that exhibit non-increasing absolute risk aversion to examine the e ects of risk aversion, price uncertainty, and other parameters on the optimal investment decision.We nd that risk aversion reduces investment, particularly if the investment size is large.Moreover, we nd that a rise in price uncertainty increases the value of deferring irreversible investments.This e ect is stronger for high levels of risk aversion.In addition, we provide, for the rst time, closed-form comparative statics formulas for the risk neutral investor.
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TL;DR: This paper found that when faced with a decision how to split their investment between a risky lottery and an asset with a fixed return, people increase the proportion invested in the risky option the more they like the lottery.
Abstract: We study the following basic intuition: when faced with a decision how to split their investment between a risky lottery and an asset with a fixed return, people increase the proportion invested in the risky option the more they like the lottery. We find counter-examples to this, and in fact we find no simple relation between preferences between lotteries and the fraction invested in them. We use three well-documented biases (ambiguity aversion, the illusion of control and myopic loss aversion) to show this. First we replicate the previous results in a laboratory experiment with financial incentives, and then test whether participants are willing to explicitly pay a small sum of money in line with the bias (pay for less ambiguity, more perceived control, or more frequent information about portfolio performance). We then study how portfolio choice depends on these biases. With the parameters chosen, the illusion of control was eliminated when participants were asked to pay to gain more control, and the bias did not affect investment behavior (i.e., participants invested in a risky option the same fraction when faced with more or less control). In the ambiguity treatment, people were willing to pay for less ambiguity, but again the level of ambiguity did not influence investment. Finally, in the myopic loss aversion treatment participants were willing to pay money to have more freedom to choose, even though (in line with the documented bias) they invested less when having more freedom to change their investment.
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TL;DR: In this paper, it was shown that the total expected payoff to a player over games with mixed equilibria is higher if this player is risk averse than if he is risk neutral provided that all games are played with the same probability.
Abstract: Simulations indicated that, in the class of 2 x 2 games which only have a mixed equilibrium, payoffs are increased by risk aversion compared to risk neutrality. In this paper I show that the total expected payoff to a player over this class in equilibrium is indeed higher if this player is risk averse than if he is risk neutral provided that all games are played with the same probability. Furthermore, I show that for two subclasses of games more risk aversion is always better, while for a third subclass an intermediate level of risk aversion is preferable.
TL;DR: In this paper, the qualitative concept of risk aversion is defined in terms of a preference relation on a set of probability distributions and quantitatively expressed by representing functionals (risk measure).
Abstract: The qualitative concept of the risk aversion is defined in terms of a preference relation on a set of probability distributions. Risk aversion is quantitatively expressed in terms of representing functionals (risk measure). The relationship between risk aversion and stochastic dominance is investigated. Formulas for computing risk aversion in a perturbed probability model are derived and numerical examples are given.
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TL;DR: In this article, the authors develop a Savage-type model of choice under uncertainty in which agents identify uncertain prospects with subjective compound lotteries, and show the equivalence of aversion to this risk with issue preference, the Ellsberg paradox, and uncertainty aversion.
Abstract: We develop a Savage-type model of choice under uncertainty in which agents identify uncertain prospects with subjective compound lotteries. Our theory permits issue preference; that is, agents may not be indifferent among gambles that yield the same probability distribution if they depend on different issues. Hence, we establish subjective foundations for the Anscombe-Aumann framework and other models with two different types of probabilities. We define second-order risk as risk that resolves in the first stage of the compound lottery and show the equivalence of aversion to this risk with issue preference, the Ellsberg paradox, and uncertainty aversion
24 Oct 2003
TL;DR: In this paper, the conditions under which a convex capacity (or a non-additive probability which exhibts uncertainty aversion) can be represented as a squeeze of a(n) (additive) probability measure associate to an uncertainty aversion function are investigated.
Abstract: In this paper I will investigate the conditions under which a convex capacity (or a non-additive probability which exhibts uncertainty aversion) can be represented as a squeeze of a(n) (additive) probability measure associate to an uncertainty aversion function. Then I will present two alternatives formulations of the Choquet integral (and I will extend these formulations to the Choquet expected utility) in a parametric approach that will enable me to do comparative static exercises over the uncertainty aversion function in an easy way.
01 Jan 2003
TL;DR: In this article, the equivalence of two measures of risk aversion for a general class of mean-variance preferences is established, and the implications for problems of choice under uncertainty such as portfolio choice problems are derived.
Abstract: This paper proves an analogue of Pratt's theorem for two measures of risk aversion for mean-variance preferences. A direct link is established between these measures and standard measures of risk aversion. Implications for problems of choice under uncertainty such as portfolio choice problems are derived. This paper establishes the equivalence of two measures of risk aversion for a general class of mean-variance preferences. It further derives implications for decision making under uncertainty, and establishes portfolio characterization of risk aversion for mean- variance preferences, which allows for comparison of agents' attitudes toward risk based on the choices they make under uncertainty. The motivation for studying mean-variance preferences is twofold: 1) they are widely used in finance; and 2) Epstein (1985) has shown that in the class of Machina's (1982) non-expected utility preferences only mean-variance preferences satisfy appropriate decreasing-absolute- risk-aversion conditions.
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TL;DR: In this article, the authors determined the precise connection between an agent's attitude towards income risks and his attitude over risks in the underlying consumption space, following a general mathematical theory connecting the curvature properties of an objective function with the ray-curvature property of its dual.
Abstract: This note determines the precise connection between an agent`s attitude towards income risks and his attitude over risks in the underlying consumption space. Our results follow a general mathematical theory connecting the curvature properties of an objective function with the ray-curvature properties of its dual.
TL;DR: In this article, the authors address the topic of price stickiness, that is price elasticity below one with respect to nominal shocks, in a general equilibrium setting where ambiguity and weak rational expectations are allowed.
Abstract: The paper address the topic of price stickiness, that is price elasticity below one with respect to nominal shocks. The paper original contribution is also in its approach to modelling: hard uncertainty and macroeconomics are linked within a micro-founded framework. The analysis is carried out in a general equilibrium setting where ambiguity and weak rational expectations are allowed. Ambiguity is introduced in the form of firms lack of knowledge about the relationship between changes in the aggregated stock of money and changes in money distribution across the heterogeneous consumers that populate the economy. It is shown that price stickiness can be generated with rational agents, even in the case a change of the money level does not alter money distribution, by assuming that firms attitude towards ambiguity is asymmetric: ambiguity aversion towards potential positive outcomes and ambiguity seeking towards negative ones. Such asymmetric attitude towards ambiguity is not arbitrary but finds some support in empirical research about economic behaviour.