Showing papers on "Ambiguity aversion published in 1997"
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TL;DR: In this article, the authors extend the Nash equilibrium solution concept for strategic form games to include loss aversion characteristics of the players, and show existence of loss aversion equilibrium for any extended game, and compare it to Nash equilibrium.
Abstract: The Nash equilibrium solution concept for strategic form games is based on the assumption of expected utility maximization. Reference dependent utility functions (in which utility is determined not only by an outcome, but also by the relationship of the outcome to a reference point) are a better predictor of behavior than expected utility. In particular, loss aversion is an important element of such utility functions. We extend strategic form games to include loss aversion characteristics of the players. We define loss-aversion equilibrium, a solution concept endogenizing reference points. Reference points emerge as expressions of anticipation which are fulfilled in equilibrium. We show existence of loss aversion equilibrium for any extended game, and compare it to Nash equilibrium. Comparative statics show that an increase in loss aversion of one player can affect his and other players’ payoffs in different directions.
166 citations
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TL;DR: In this article, the authors show that ambiguity aversion can explain the existence of incomplete contracts in the investment hold-up model, where the decision maker adjusts his choice on the side of caution in response to his imprecise knowledge of the odds.
Abstract: Subjective uncertainty is characterized by ambiguity if the decision maker has an imprecise knowledge of the probabilities of payoff relevant events. In such an instance, the decision maker's beliefs are better represented by a set of probability functions than by a unique probability function. An ambiguity averse decision maker adjusts his choice on the side of caution in response to his imprecise knowledge of the odds. The non-additive expected utility model allows a formal characterization of such behaviour. Using this model, this paper shows that ambiguity aversion can explain the existence of incomplete contracts. The setting for the demonstration is the investment hold-up model which has been the focus of much of the recent research on the implications of incomplete contracts.
160 citations
TL;DR: This paper showed that if two individuals have different prior beliefs about some event, and two-sided private information, then each individual's willingness to bet will exhibit a bid ask spread property.
Abstract: People are less willing to accept bets about an event when they do not know the true probability of that event. Such “uncertainty aversion” has been used to explain certain economic phenomena. This paper considers how far standard private information explanations (with strategic decisions to accept bets) can go in explaining phenomena attributed to uncertainty aversion. This paper shows that if two individuals have different prior beliefs about some event, and two sided private information, then each individual’s willingness to bet will exhibit a bid ask spread property. Each individual is prepared to bet for the event, at sufficiently favorable odds, and against, at sufficiently favorable odds, but there is an intermediate range of odds where each individual is not prepared to bet either way. This is only true if signals are distributed continuously and sufficiently smoothly. It is not true, for example, in a finite signal model.
42 citations
TL;DR: In this paper, a parametric representation of uncertainty aversion is proposed by means of a special class of fuzzy measures, known as g λ-measures, and the parameter λ may be considered an indicator of uncertainty.
Abstract: A recent stream of literature has suggested that many market imperfections or ‘puzzles’ can be easily explained once information ambiguity, or knightian uncertainty is taken into account. Here we propose a parametric representation of this concept by means of a special class of fuzzy measures, known as g λ-measures. The parameter λ may be considered an indicator of uncertainty. Starting with a distribution, a value λ in (0, ∞) and a benchmark utility function we obtain a sub-additive expected utility, representing uncertainty aversion. A dual value λ∗ in (−1, 0) defining a super-additive expected utility is also recovered, while the benchmark expected utility is obtained for λ = λ∗ = 0. The two measures may be considered as lower and upper bounds of expected utility with respect to a set of probability measures, in the spirit of Gilboa-Schmeidler MMEU theory and of Dempster probability interval approach. The parametrization may be used to determine the effect of information ambiguity on asset prices in a ...
38 citations
TL;DR: In this paper, the authors use genetic algorithms to show that risk aversion and some related consequences emerge naturally as a result of evolutionary pressures, and characterize optimizing under uncertainty as surfing in a fitness seascape.
Abstract: Economic decision making under uncertainty is universally characterized by aversion to risk. One of the most basic concepts in economic theory, risk aversion is usually explained by the concavity of the utility function, which, in turn, is based on a person's satiability for wealth. I use genetic algorithms to show that risk aversion, and some related consequences, emerge naturally as a result of evolutionary pressures. In analogy to the well-known hillclimbing metaphor, it is helpful in this context to characterize optimizing under uncertainty as “surfing in a fitness seascape.” © 1997 John Wiley & Sons, Inc.
37 citations
TL;DR: In this article, the representative investor's coefficient of relative risk aversion using option price data is estimated using the method of simulated moments, which is carried out using the following assumptions: agents have constant proportional risk averse preferences, complete markets exist, and asset returns are distributed lognormally.
Abstract: This paper estimates the representative investor's coefficient of relative risk aversion using option price data. Estimation is carried out using the method of simulated moments. Employing the following assumptions: a) agents have constant proportional risk averse preferences, b) complete markets exist, and c) asset returns are distributed lognormally, an objective function is constructed within the equivalent martingale measure framework. Unlike the case of equity markets, the implied risk aversion parameter from option prices is quite low and stays between zero and one.
31 citations
TL;DR: In this paper, a definition of uncertainty aversion for nonprobabilistic decision models based on set comparisons is proposed and dual results are obtained for uncertainty appeal, and it is shown that imposing an uncertainty-neutrality condition leads to an impossibility result.
20 citations
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TL;DR: The authors proposed a notion of absolute ambiguity aversion by building on the notion of comparative ambiguity aversion, and characterized it for a preference model which encompasses some of the most popular models in the literature.
Abstract: The theory of subjective expected utility (SEU) has been recently extended to allow ambiguity to matter for choice. We propose a notion of absolute ambiguity aversion by building on a notion of comparative ambiguity aversion. We characterize it for a preference model which encompasses some of the most popular models in the literature. We next build on these ideas to provide a definition of unambiguous act and event, and show the characterization of the latter. As an illustration, we consider the classical Ellsberg 3-color urn problem and find that the notions developed in the paper provide intuitive answers.
18 citations
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TL;DR: In this paper, the consequences of non-additive expected utility on risk sharing and equilibrium in a general equilibrium set-up were explored, and it was shown that convexity of an agent's preferences is equivalent to the convexness of his capacity and concavity of his utility index.
Abstract: This paper explores the consequences of non-additive expected utility on risk-sharing and equilibrium in a general equilibrium set-up We establish that convexity of an agent's preferences (or strong uncertainty aversion) is equivalent to the convexity of his capacity and concavity of his utility index We also characterize a weaker form of uncertainty aversion
16 citations
10 citations
TL;DR: In this article, a decision-maker who follows the Savage axioms can appear to an outsider as if his/her subjective probabilities are non-additive, and the induced preferences can have the rank dependent expected utility form.
Abstract: In this paper we suggest a new interpretation of non-additive probabilities. We study a decision-maker who follows the Savage axioms. We show the if (s)he is able to take unobservable actions which influence the probabilities of outcomes then it can appear to an outsider as if his/her subjective probabilities are non-additive. We make a related analysis of models with objective probabilities and show that the induced preferences can have the rank dependent expected utility form. Implications for multi-period decisions are explored.
TL;DR: The authors characterizes a family of preference relations over uncertain prospects that are dynamically consistent in the Machina sense and moreover for which the updated preferences are also members of this family and can simultaneously accommodate Ellsberg-and Allais-type paradoxes.
Abstract: This article characterizes a family of preference relations over uncertain prospects that (a) are dynamically consistent in the Machina sense and, moreover, for which the updated preferences are also members of this family and (b) can simultaneously accommodate Ellsberg- and Allais-type paradoxes. Replacing the “mixture independence” axiom by “mixture symmetry,” proposed by Chew, Epstein, and Segal (1991) for decision making under objective risk, and requiring that for some partition of the state space the agent perceives ambiguity and so prefers a randomization over outcomes across that partition (proper uncertainty aversion), preferences can be represented by a (proper) quadratic functional. This representation may be further refined to allow a separation between the quantification of beliefs and risk preferences that is closed under dynamically consistent updating.
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TL;DR: In this paper, the authors study the properties of a general equilibrium model with purely microeconomic risk, in which agents behave according to Choquet expected utility (i.e., they maximize a non-additive expected utility).
Abstract: This paper studies the properties of a general equilibrium model with purely microeconomic risk, in which agents behave according to Choquet expected utility (i.e., they maximize a non-additive expected utility). This formalization represents a behavior exhibiting uncertainty aversion or pessimism. Under the assumption that there is a minimal consensus in the economy, it is shown that agents are fully insured at an equilibrium, that the equilibrium allocation is indeterminate, and that the size of the equilibrium set increases with the degree of uncertainty aversion.
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TL;DR: In this article, the relationship between bounded rationality and risk aversion has been studied and it is shown that bounded rationality increases risk aversion at the reference income level and that there exists an income level below the reference level where bounded rationality reduces risk aversion and may lead to risks loving behaviour.
Abstract: This paper describes the relationship between bounded rationality and risk aversion It shows athat bounded rationality increases risk aversion at the reference income level and that there exists an income level below the reference income level where bounded rationality reduces risk aversion and may lead to risks loving behaviour These theoretical results are in line with previous experimental results A boundedly rational decision maker is modelled as an agent who makes decision errors in choosing the optimal consumption bundle or does not know precisely his/her own true preference ordering
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TL;DR: In this paper, the authors explore the beliefs implicit in the equilibrium behavior of the players in a game where the players have non-additive beliefs and show that there are well defined departures from common knowledge of the game among the players.
Abstract: In a game where the players have non-additive beliefs, we explore the beliefs implicit in the equilibrium behaviour of the players. Under one interpretation, we can show that there are well-defined departures from common knowledge of the game among the players. Our argument revolves around a representation theorem which relates equilibrium under under non-additive beliefs to equilibrium actions of a set of types in a Bayesian game with a common prior. Among these types, the game is common p-belief, where the 'p' depends on the degree of uncertainty aversion. Only when the beliefs are additive is p=1.
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TL;DR: In this article, the authors derive a class of utility functions that are equivalent with respect to a well-defined functional form and apply a general view of constant relative risk aversion to investigate on different equivalence relations.
Abstract: We derive a class of utility functions that are equivalent with respect to a well-defined functional form. We apply a general view of constant relative risk aversion to investigate on different equivalence relations. Then we compare our results with standard applications in economics and finance.
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TL;DR: In this paper, the same authors prove several representation theorems, where constant risk aversion is combined with some other known axioms to imply specific functional forms, and prove that adding the same constant to all outcomes of two distributions, or multiplaying all their outcomes by the same positive constant, will not change the preformence relation between them.
Abstract: Constant risk aversion means that adding the same constant to all outcomes of two distributions, or multiplaying all their outcomes by the same positive constant, will not change the preformence relation between them. In this paper we prove several representation theorems, where constant risk aversion is combined with some other known axioms to imply specific functional forms.
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01 Jan 1997
TL;DR: In this paper, the consequences of non-additive expected utility on risk sharing and equilibrium in a general equilibrium set-up were explored, and it was shown that convexity of an agent's preferences (or strong uncertainty aversion) is equivalent to the convexness of his capacity and concavity of his utility index.
Abstract: This paper explores the consequences of non-additive expected utility on risk-sharing and equilibrium in a general equilibrium set-up. We establish that convexity of an agent's preferences (or strong uncertainty aversion) is equivalent to the convexity of his capacity and concavity of his utility index. We also characterize a weaker form of uncertainty aversion.
Posted Content•
01 Jan 1997
01 Jan 1997
TL;DR: In this paper, the authors consider a class of binary relations on a set of Anscombe-Aumann acts, each admitting a Choquet-expected utility representation, and propose rationality postulates, centered on Myerson's Subjective Substitution axiom, which characterize the given class as one of dynamically consistent, or coherent, conditional preferences.
Abstract: I consider a class of binary relations on a set of Anscombe-Aumann acts, each admitting a Choquet-expected utility representation, and propose a set of rationality postulates, centered on Myerson’s Subjective Substitution axiom, which characterize the given class as one of dynamically consistent, or coherent, conditional preferences. I show that, under regularity conditions, if a system of conditional preference relations is coherent then (1) unconditional preferences must satisfy Savage’s Sure Thing Principle, and (2) conditioning with respect to non-null events conforms to Savage’s Bayesian update rule; the converse is also true whenever the conditioning events are non-null. In view of the results obtained, a notion of partial dynamic consistency is introduced and shown to accomodate violations of the Sure Thing Principle.