reference dependent ambiguity abstract motivated by experimental and empirical evidence i study a framework where reference points such as a status quo endowment or default option can distort the way an individual responds to ambiguity i characterize a model of reference dependent maxmin expected utility and provide behavioral foundations for comparing reference dependent ambiguity attitudes i also illustrate some implications of reference dependent ambiguity for trade in an asset market including underdiversification no trade and the potential for a market collapse

indecisiveness in behavioral welfare economics abstract when an individual s preferences depend on the time or frame at which decisions are made the preferences that appear at different frames must be aggregated in order to make social decisions suppose we aggregate each individual i s frame based preferences with a behavioral welfare relation that ranks x above y if when both x and y are available i sometimes choose x and not y and never chooses y and not x the set of pareto optima can then be large in fact a small amount of preference diversity across frames can cause every allocation to be pareto optimal more generally the set of pareto optima will have the same dimension as the set of allocations the pareto criterion then will not be able to discriminate locally among policy options a small distortion for example will call for no policy response

on the indifference relation in bewley preferences abstract bewley s 2002 influential model of preferences over uncertain prospects features an incomplete preference relation and a set of priors over the states of the world such that one act is preferred to another if and only if its expected utility is higher under every prior in that set this note shows that under general conditions on preferences the decision maker in the bewley model cannot be indifferent between distinct monetary acts whenever the set of priors is fully dimensional in the special case of two states in particular such objectively rational preferences are incomplete if and only if the indifference relation is trivial in the above sense

randomization vs selection how to choose in the absence of preference decision makers sometimes have to choose between alternative options about which they have no preference either they judge the options equally valuable indifference or they have no judgment about their relative value noncomparability choosing randomly is generally considered a natural way to deal with such situations this paper shows however that systematic randomization between noncomparable options may lead to a chain of decisions resulting in monetary losses a money pump furthermore these losses can be avoided by deliberately selecting one of the noncomparable options instead of randomizing thus randomization among noncomparable options is costly relative to deliberate selection on the other hand randomization among indifferent options is costless relative to deliberate selection

uncertainty and risk in financial markets this paper considers a general equilibrium model in which the distinction between uncertainty and risk is formalized by assuming agents have incomplete preferences over statecontingent consumption bundles as in bewley 1986 without completeness individual decision making depends on a set of probability distributions over the state space a bundle is preferred to another if and only if it has larger expected utility for all probabilities in this set when preferences are complete this set is a singleton and the model reduces to standard expected utility in this setting we characterize pareto optima and equilibria and show that the presence of uncertainty generates robust indeterminacies in equilibrium prices and allocations for any specification of initial endowments we derive comparative statics results linking the degree of uncertainty with changes in equilibria despite the presence of robust indeterminacies we show that equilibrium prices and allocations vary continuously with underlying fundamentals equilibria in a standard risk economy are thus robust to adding small degrees of uncertainty finally we give conditions under which some assets are not traded due to uncertainty aversion

robust social decisions we propose and operationalize normative principles to guide social decisions when individuals potentially have imprecise and heterogeneous beliefs in addition to conflicting tastes or interests to do so we adapt the standard pareto principle to those preference comparisons that are robust to belief imprecision and characterize social preferences that respect this robust principle we also characterize a suitable restriction of this principle the former principle provides stronger guidance when it can be satisfied when it cannot the latter always provides minimal guidance

ambiguity aversion and comparative ignorance decisions under uncertainty depend not only on the degree of uncertainty but also on its source as illustrated by ellsberg s observation of ambiguity aversion in this article we propose the comparative ignorance hypothesis according to which ambiguity aversion is produced by a comparison with less ambiguous events or with more knowledgeable individuals this hypothesis is supported in a series of studies showing that ambiguity aversion present in a comparative context in which a person evaluates both clear and vague prospects seems to disappear in a noncomparative context in which a person evaluates only one of these prospects in isolation

knightian uncertainty and moral hazard abstract this paper presents a principal agent model in which the agent has imprecise beliefs we model this situation formally by assuming the agent s preferences are incomplete as in bewley 1986 2 in this setting incentives must be robust to knightian uncertainty we study the implications of robustness for the form of the resulting optimal contracts we give conditions under which there is a unique optimal contract and show that it must have a simple flat payment plus bonus structure that is output levels are divided into two sets and the optimal contract pays the same wage for all output levels in each set we derive this result for the case in which the agent s utility function is linear and then show it also holds if this utility function has some limited curvature

ambiguity aversion and incompleteness of financial markets it is widely thought that incomes risks can be shared by trading in financial assets but financial assets typically carry some risk idiosyncratic to them hence disposing incomes risk using financial assets will involve buying into the inherent idiosyncratic risk however standard theory argues that diversification would reduce the inconvenience of idiosyncratic risk to arbitrarily low levels this argument is less robust than what standard theory leads us to believe ambiguity aversion can exacerbate the tension between the two kinds of risks to the point that classes of agents may not want to trade some financial assets thus theoretically the effect of ambiguity aversion on financial markets is to make the risk sharing opportunities offered by financial markets less complete than it would be otherwise

financial complexity and trade what are the implications on trading activity if investors are not sophisticated enough to understand and evaluate trades that have a complex payoff structure can frictions generated by this type of financial complexity be so severe that they lead to a complete market freeze like that of the recent financial crisis starting from an allocation that is not pareto optimal we find that whether complexity impedes trade depends on how investors perceive risk and uncertainty for smooth convex preferences such as subjective expected utility complexity cannot halt trade even in the extreme case where each investor is so unsophisticated that he can only trade up to one arrow debreu security without being able to combine two or more in order to construct a complex trade however for non smooth preferences which allow for kinked indifference curves such as maxmin expected utility complexity can completely shut down trade

pareto optima and equilibria when preferences are incompletely known an exchange economy in which agents have convex incomplete preferences defined by families of concave utility functions is considered sufficient conditions for the set of efficient allocations and equilibria to coincide with the set of efficient allocations and equilibria that result when each agent has a utility in her family are provided welfare theorems in an incomplete preferences framework therefore hold under these conditions and efficient allocations and equilibria are characterized by first order conditions

ambiguity and uncertainty in ellsberg and shackle this paper argues that the similarities between ellsberg s and shackle s frameworks for discussing the limits of the probabilistic approach to decision theory are more important than usually admitted the paper discusses the grounds on which the ambiguity surrounding the decision maker in ellsberg s urn experiments can be deemed analogous to the uncertainty faced by shackle s entrepreneur taking crucial decisions the two authors insights are assessed and special attention is paid to the criteria for decision under uncertainty they put forward the paper establishes a link between ellsberg s and shackle s perspectives and the non additive probability approach of gilboa and schmeidler an approach that offers an alternative to standard probability calculus which can be of use to analyse both ambiguity and uncertainty the comparison between ellsberg and shackle draws on an interpretation of keynes s treatise on probability emphasising keynes s rejection of both well defined probability functions and maximisation as a guide to human conduct it is shown that keynes s viewpoint implies a reconsideration of the boundaries of probability theory that is in the same vein of ellsberg s and shackle s concern in the years of the consolidation of savage s new probabilistic mainstream copyright the author 2009 published by oxford university press on behalf of the cambridge political economy society all rights reserved oxford university press

intertemporal equilibria with knightian uncertainty we study a dynamic and infinite dimensional model with incomplete multiple prior preferences in interior efficient allocations agents share a common risk adjusted prior and subjective interest rate interior efficient allocations and equilibria coincide with those of economies with subjective expected utility and priors from the agents multiple prior sets a specific model with neither risk nor uncertainty at the aggregate level is considered risk is always fully insured for small levels of ambiguity there exists an equilibrium with inertia where agents also insure fully against knightian uncertainty when the level of ambiguity exceeds a critical threshold full insurance no longer prevails and there exist equilibria with inertia where agents do not insure against uncertainty at all we also show that equilibria with inertia are indeterminate

interim efficient allocations under uncertainty abstract this paper considers an exchange economy under uncertainty with asymmetric information uncertainty is represented by multiple priors and posteriors of agents who have either bewley s incomplete preferences or gilboa schmeidler s maximin expected utility preferences the main results characterize interim efficient allocations under uncertainty that is they provide conditions on the sets of posteriors thus implicitly on the way how agents update the sets of priors for non existence of a trade which makes all agents better off at any realization of private information for agents with the incomplete preferences the condition is necessary and sufficient but for agents with the maximin expected utility preferences the condition is sufficient only a couple of necessary conditions for the latter case are provided

the uncertain foundations of the welfare state abstract the welfare state is often portrayed as provider of insurance against uncertainties in knight s 1921 sense of the term which would be refused or underinsured on private markets this image conflicts with the standard economic model of risk exchange founded on the subjective interpretation of probability which predicts that all individual uncertainties will be insured by private markets our aim in this paper is to explain why this prediction fails and building on contributions to decision theory that take seriously the idea of knightian uncertainty to show why social insurance may be justified

sharing risk and ambiguity we study the market implications of ambiguity in common models we show that generic determinacy is a robust feature in general equilibrium models that allow a distinction between ambiguity and risk

the existence and efficiency of general equilibrium with incomplete markets under knightian uncertainty abstract this paper first establishes the existence of equilibrium for an economy with knightian uncertainty and incomplete markets and then demonstrates the constrained pareto efficiency of the equilibrium when there is one commodity only in each state of nature

incomplete preferences and equilibrium in contingent markets this paper shows that betting or speculative trading between agents with incomplete preferences is likely to occur if agents have access to convex choice sets this contrasts sharply with endowment economy models where preference incompleteness often hinders betting speculative trading or mutually beneficial insurance arrangements our results imply that decision makers with identical tastes and identical feasible sets will potentially gain from speculative trade for generic status quo allocations we also develop a framework for endogenizing the status quo allocations of decision makers that are treated exogenously in the existing literature finally we provide a tractable differential representation of status quo allocations equilibria and conditions where speculative trade may or may not emerge

risk management strategies via minimax portfolio optimization recent extreme economic developments nearing a worst case scenario motivate further examination of minimax linear programming approaches for portfolio optimization risk measured as the worst case return is employed and a portfolio from maximizing returns subject to a risk threshold is constructed minimax model properties are developed and parametric analysis of the risk threshold connects this model to expected value along a continuum revealing an efficient frontier segmenting investors by risk preference divergence of minimax model results from expected value is quantified and a set of possible prior distributions expressing a degree of knightian uncertainty corresponding to risk preference determined the minimax model will maximize return with respect to one of these prior distributions providing valuable insight regarding an investor s risk attitude and decision behavior linear programming models for financial firms to assist individual investors to hedge against losses by buying insurance and a model for designing variable annuities are proposed

interim efficiency with meu preferences abstract recently kajii and ui 2009 17 proposed to characterize interim efficient allocations in an exchange economy under asymmetric information when uncertainty is represented by multiple posteriors when agents have bewley s incomplete preferences kajii and ui 2009 17 proposed a necessary and sufficient condition on the set of posteriors however when agents have gilboa schmeidler s maxmin expected utility preferences they only propose a sufficient condition the objective of this paper is to complete kajii and ui s work by proposing a necessary and sufficient condition for interim efficiency for various models of ambiguity aversion and in particular maxmin expected utility our proof is based on a direct application of some results proposed by rigotti shannon and stralecki 2008 24

a more robust definition of subjective probability the goal of choice theoretic derivations of subjective probability is to separate a decisionmaker s underlying beliefs subjective probabilities of events from their preferences attitudes toward risk classical derivations have all relied upon some form of the marschak samuelson independence axiom or the savage sure thing principle which imply that preferences over lotteries conform to the expected utility hypothesis this paper presents a choice theoretic derivation of subjective probability in a savage type setting of purely subjective uncertainty which neither assumes nor implies that the decisionmaker s preferences over lotteries necessarily conform to the expected utility hypothesis copyright 1992 by the econometric society

ambiguity aversion decreases the impact of partial insurance evidence from african farmers indemnifying smallholder farmers against crop loss is thought to play an important role in encouraging the adoption of new technologies and facilitating productivity growth but to be infeasible due to information problems consequently there is interest in developing alternative partial insurance products examples include rainfall insurance and the limited liability inherent in credit contracts i argue that although these products may reduce information asymmetry ambiguity averse farmers struggle to assess whether the contracts reduce risk this problem is most pronounced when the production technology is ambiguous as is likely the case for new technologies i formalize this argument and test the theory using data from two rcts conducted in malawi and kenya comparative statics from the theory are consistent with both sets of data and i argue that income losses from ambiguity aversion may be substantial

markets in environmental governance from theory to practice abstract the aim of this paper is to clarify what is meant by markets for ecosystem services es the defining characteristic of markets is interaction through trade two main dimensions are identified as basis for classifying markets in es firstly we have markets with and without intermediaries secondly some markets for es are created by defined liabilities like caps on emissions while other trades come about voluntarily altogether six forms of markets are identified with two being incomplete the paper also offers an analysis of the most important existing markets for es using the developed classification regarding payments for ecosystem services pes most are not markets not even incomplete this is so as most resources are raised through taxes or fees command not trade moreover most payments are best characterized as subsidies cap and trade systems like those for carbon qualify as markets but depend crucially on the politically defined cap moreover it is this cap that protects the environment while the idea with markets in es is to escape command and control it is observed that c c is essential for these markets to work

preference reversals for ambiguity aversion this paper finds preference reversals in measurements of ambiguity aversion even if psychological and informational circumstances are kept constant the reversals are of a fundamentally different nature than the reversals found before because they cannot be explained by context dependent weightings of attributes we offer an explanation based on sugden s random reference theory with different elicitation methods generating different random reference points then measurements of ambiguity aversion that use willingness to pay are confounded by loss aversion and hence overestimate ambiguity aversion this paper was accepted by teck ho decision analysis

decision theory under ambiguity we review recent advances in the field of decision making under uncertainty or ambiguity we start with a presentation of the general approach to a decision problem under uncertainty as well as the standard bayesian treatment and issues with this treatment we present more general approaches choquet expected utility maximin expected utility smooth ambiguity and so forth that have been developed in the literature under the name of models of ambiguity sensitive preferences we draw a distinction between fully subjective models and models incorporating explicitly some information we review definitions and characterizations of ambiguity aversion in these models we mention the challenges posed by some of the models presented we end with a review of part of the experimental literature and applications of these models to economic settings

subjective beliefs and ex ante trade we study a definition of subjective beliefs applicable to preferences that allow for the perception of ambiguity and provide a characterization of such beliefs in terms of market behavior using this definition we derive necessary and sufficient conditions for the efficiency of ex ante trade and show that these conditions follow from the fundamental welfare theorems when aggregate uncertainty is absent our results show that full insurance is efficient if and only if agents share some common subjective beliefs our results hold for a general class of convex preferences which contains many functional forms used in applications involving ambiguity and ambiguity aversion we show how our results can be articulated in the language of these functional forms confirming results existing in the literature generating new results and providing a useful tool for applications

robust permanent income and pricing i suppose there exists an extremely powerful and if i may so speak malignant being whose whole endeavours are directed toward deceiving me rene descartes meditations ii 1

asymmetric information nonadditive expected utility and the information revealed by prices an example i develop a simple example of a model in which agents have asymmetric information and preferences that are represented by a nonadditive expected utility function the a priori uninformed agent after observing the equilibrium price has conditional beliefs that remain nonadditive then even when the equilibrium price function is fully revealing i e one to one it may be worth while for an a priori uninformed agent to buy redundant private information if he is more confident in that information than in that revealed by the price system

when does aggregation reduce risk aversion we study the problem of risk sharing within a household or syndicate a household shares risky prospects using a social welfare functional we characterize the social welfare functionals such that the household is collectively less risk averse than each member and satisfies the pareto principle and an invariance axiom we single out the sum of certainty equivalents as the unique member of this family which is quasiconcave over riskless allocations

the asymmetric stabilizing effects of price flexibility historical evidence and implications the evidence of business cycles across a sample of industrial countries indicates asymmetry in the output and price adjustments to aggregate demand shocks in the pre and post war periods upward price flexibility is significant in moderating output fluctuations across countries in the pre and post war periods nonetheless the effect of upward price flexibility in accelerating trend price inflation is more evident across countries in the post war period compared to the pre war period the combined evidence is consistent with a steeper supply curve in the face of expansionary demand shocks that increases the stabilizing effect of upward price flexibility in contrast a flatter supply curve in the face of negative demand shocks has countered the stabilizing function of downward price flexibility which appears insignificant across countries in the pre and post war periods in addition a slower demand response to price change during recessions has further reinforced the contractionary effect on output d

ambiguity made precise a comparative foundation the theory of subjective expected utility 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 journal of economic literature classification number d81

efficient allocations under ambiguity abstract important implications of the expected utility hypothesis and risk aversion are that if agents have the same probability belief then consumption plans in every efficient allocation of resources under uncertainty are comonotone with the aggregate endowment and if their beliefs are concordant then the consumption plans are measurable with respect to the aggregate endowment we study these two properties of efficient allocations for models of preferences that exhibit ambiguity aversion using the concept of conditional beliefs which we introduce in this paper we provide characterizations of such conditional beliefs for the standard models of preferences used in applications

product differentiation decisions under ambiguous consumer demand and pessimistic expectations abstract this paper studies product differentiation decisions in a spatial duopoly with limited information on consumer demand in particular a situation is discussed in which the firms do not know the exact distribution of the random location of consumer demand and its responsiveness to price changes measured by the scale of transport costs but resolve the resulting ambiguity using the maxmin or minimax regret criteria when the firms are sufficiently pessimistic is high enough results are in contrast with the existing literature in particular an increase of demand location uncertainty decreases the equilibrium product differentiation intensifying the second stage competition in prices although the effect is dampened by uncertainty about transport costs endogenizing the choice of objective function leads to the dominance of an extreme form of pessimism which turns out to be socially optimal