attitudes to uncertainty in a strategic setting much uncertainty in life relates to the behaviour of others in interactive environments this article tests some implications of subjective expected utility theory savage 1954 in an experimental strategic setting where there is uncertainty about the actions of other players in this environment a large majority of our participants violate subjective expected utility theory however they do not exhibit the sorts of consistent attitude to ambiguity found in individual decision experiments we discuss three possible explanations of their behaviour non linear transformation of probabilities noise in responses and or systematic biases in the way that individuals generate subjective probabilities

preference reversals and the independence axiom of all of the paradoxical patterns of behavior reported in laboratory experiments one of the most perplexing for decision theorists is the preference reversal phenomenon a subject in a preference reversal experiment is typically given a choice between a lottery with a high probability of winning a modest amount of money a p bet and a lottery with a low probability of winning a large amount of money a bet the lowest amount of money for which the subject would willingly sell either of these lotteries is also elicited the most common reversal is for a subject to choose the p bet over the bet but to put a higher selling price on the bet preference reversals were first reported by harold lindman 1971 and sarah lichtenstein and paul slovic 1971 in discussing the psychologists discovery of such reversals david grether and charles plott remark the inconsistency is deeper than mere lack of transitivity or even stochastic transitivity it suggests that no optimization principles of any sort lie behind even the simplest of human choices 1979 p 623 this paper offers a simple alternative explanation of documented preference reversals an explanation that does not require the abandonment of the transitivity assumption

the disparity between willingness to accept and willingness to pay measures of value psychologists have long argued that people are much more averse to a loss than attracted to an equivalent gain this behavior termed loss aversion has been formalized by kahneman and tversky 1979 in their reformulation of expected utility theory prospect theory in prospect theory the utility function is replaced by a value function that evaluates changes in income from the current level increases in income are weighted by a relatively small marginal utility decreases in income are weighted by a much larger marginal utility in effect the value function implies that a kink in the relationship between utility and income occurs at the initial income or reference point and that the slope of the utility function for losses in income is steeper than it is for gains in a recent paper knetsch and sinden 1984 report a series of experiments that demonstrate the existence of a large disparity between willingness to accept wta and willingness to pay wtp measures of value they argue that the psychological theory of loss aversion explains this difference economic theory would suggest that individuals who exhibit a large disparity between wta and wtp are perhaps underperceiving the value of gains or overperceiving the value of losses are behaving in an irrational manner and will consequently achieve a lower level of well being than if they behaved in a true utility maximizing manner this would in contrast to loss aversion usually imply near equal values for wta and wtp see willig 1976 further documentation of a larger than expected disparity between wta and wtp has been obtained in surveys asking for the value of a variety of public goods for example cummings brookshire and schulze 1986 document six

asymmetric effects of favorable and unfavorable information on decision making under ambiguity most daily decisions involve uncertainty about outcome probabilities arising from incomplete knowledge i e ambiguity we explore how the addition of partial information affects these types of choices using theoretical and empirical methods our experiments in both gain and loss domains demonstrate that when such information supports a favorable outcome it strongly increases valuation of an ambiguous financial prospect however when information supports an unfavorable outcome it has significantly less impact we find that two mechanisms drive this asymmetry first unfavorable information decreases estimates of a good outcome occurring but also reduces aversive uncertainty these factors act in opposition minimizing the effects of unfavorable information second when information can be subjectively interpreted unfavorable information is less likely to be integrated into evaluations our findings reveal mechanisms not captured by traditional models of decision making under uncertainty and highlight

preference reversals under ambiguity preference reversals have been widely studied using risky or riskless gambles however little is known about preference reversals under ambiguity unknown probabilities subjects were asked to make a binary choice between ambiguous p bets big likelihood of giving small prize and ambiguous bets small likelihood of giving large prize and their willingness to accept was elicited subjects then performed the same two tasks with risky bets where the probability of winning for a given risky bet is the center of the probability interval of the corresponding ambiguous bet preference reversals are not only replicated under ambiguity but are even stronger than are those under risk this is due to higher elicited prices for the bet and lower elicited prices for the p bet under ambiguity than under risk this result can be explained by the shape of the weighting function for different levels of uncertainty and for different elicitation modes this paper was accepted by peter wakker decision analysis

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

a test of the theory of reference dependent preferences eight alternative methods of eliciting preferences between money and a consumption good are identified two of these are standard willingness to accept and willingness to pay measures these methods differ with respect to the reference point used and the dimension in which responses are expressed the loss aversion hypothesis of tversky and kahneman s theory of reference dependent preferences predicts systematic differences between the preferences elicited by these methods these predictions are tested by eliciting individuals preferences for two private consumption goods the experimental design is incentive compatible and controls for income and substitution effects the theory s predictions are broadly confirmed

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

contract nonperformance risk and uncertainty in insurance markets insurance contracts may fail to perform leading to a default on valid claims we relax the standard assumption of known probabilities for such defaults by allowing for uncertainty within a large behavioral experiment we show that introducing risk and uncertainty each leads to significant reductions in insurance demand and that the effects are comparable in magnitude 17 1 and 14 5 percentage points furthermore risk and ambiguity averse participants are affected most these findings are in line with models incorporating ambiguity attitudes or alternatively pessimistic beliefs an analysis of the belief and decision dynamics suggests persistent pessimistic priors and disregard of peer experiences leading to a stable uncertainty effect

prospect theory mental accounting and differences in aggregated and segregated evaluation of lottery portfolios if individuals have to evaluate a sequence of lotteries their judgment is influenced by the presentation mode experimental studies have found significantly higher acceptance rates for a sequence of lotteries if the overall distribution was displayed instead of the set of lotteries itself mental accounting and loss aversion provide an easy and intuitive explanation for this phenomenon in this paper we offer an explanation that incorporates further evaluation concepts of prospect theory our formal analysis of the difference in aggregated and segregated portfolio evaluation demonstrates that the higher attractiveness of the aggregated presentation mode is not a general phenomenon as suggested in the literature but depends on specific parameters of the lotteries the theoretical findings are supported by an experimental study in contrast to the existing evidence and in line with our theoretical results we find for specific types of lotteries an even lower acceptance rate if the overall distribution is displayed

a continuous time model to determine the intervention policy for pbgc abstract the pension benefit guaranty corporation pbgc which insures private defined benefit pension plans is facing mounting deficits the main cause of this predicament for pbgc can be traced down to the misuse of the insurance by a few companies we therefore propose an active intervention policy which would result in termination of severely underfunded plans for the pbgc a continuous time model is provided to help determine the point of intervention if necessary using option pricing techniques a clear exposition of the intervention doctrine is thus obtained via this model we also provide a numerical illustration of the working of the model on a hypothetical pension plan

continuous time methods in finance a review and an assessment i survey and assess the development of continuous time methods in finance during the last 30 years the subperiod 1969 to 1980 saw a dizzying pace of development with seminal ideas in derivatives securities pricing term structure theory asset pricing and optimal consumption and portfolio choices during the period 1981 to 1999 the theory has been extended and modified to better explain empirical regularities in various subfields of finance this latter subperiod has seen significant progress in econometric theory computational and estimation methods to test and implement continuous time models capital market frictions and bargaining issues are being increasingly incorporated in continuous time theory the roots of modern continuous time methods in finance can be traced back to the seminal contributions of merton 1969 1971 1973b in the late 1960s and early 1970s merton 1969 pioneered the use of continuous time modeling in financial economics by formulating the intertemporal consumption and portfolio choice problem of an investor in a stochastic dynamic programming setting merton 1973b also showed how such a framework can be used to develop equilibrium asset pricing implications thereby significantly extending the asset pricing theory to richer dynamic settings and expanding the scope of applications of continuous time methods to study problems in financial economics 1 within a span of about 30 years from the publication of merton s inf luential papers continuous time methods have become an integral part of financial economics indeed in certain core areas in finance such as e g asset pricing derivatives valuation term structure theory and portfolio selection continuoustime methods have proved to be the most attractive way to conduct research and gain economic intuition the continuous time approach in these areas has produced models with a rich variety of testable implications the econometric theory for testing continuous time models has made rapid strides in the last decade and has thus kept pace with the impressive progress on the theoretical front one hopes that the actual empirical investigations and estimation using the new procedures will follow suit soon

judgemental overconfidence self monitoring and trading performance in an experimental financial market we measure the degree of overconfidence in judgment in the form of miscalibration i e the tendency to overestimate the precision of one s information and self monitoring a form of attentiveness to social cues of 245 participants and also observe their behaviour in an experimental financial market under asymmetric information miscalibrated traders underestimating the conditional uncertainty about the asset value are expected to be especially vulnerable to the winner s curse high self monitors are expected to behave strategically and achieve superior results our empirical results show that miscalibration reduces and self monitoring enhances trading performance the effect of the psychological variables is strong for men but non existent for women

an experimental test of the under annuitization puzzle with smooth ambiguity and charitable giving abstract in a life cycle model with a bequest motive we study the impact of smooth ambiguity aversion to uncertain survival probabilities on the optimal demand for annuities we implement a theory driven laboratory experiment first a subject s ambiguity attitude is elicited in a simple experimental setting able to make the smooth ambiguity model operational then in a two period annuity bequest decision problem the subject s bequest in the second period is presented as a donation to a previously chosen charity contingent to the subject being active after the first period in line with the theoretical predictions we find that ambiguity averse resp loving subjects invest less resp more in annuities than ambiguity neutral ones furthermore subjects contingent donation to the chosen charity increases in their investment in annuities only for sufficiently high levels of warm glow altruism

reference dependent subjective expected utility abstract a reference dependent generalisation of subjective expected utility theory is presented in this theory preferences between acts depend both on final outcomes and on reference points which may be uncertain acts it is characterised by a set of axioms in a savage style framework a restricted form of the theory separates attitudes to end states encoded in a satisfaction function from attitudes to gains and losses of satisfaction given weak additional assumptions the restricted theory excludes cycles of choice explains observed disparities between willingness to pay and willingness to accept valuations of lotteries and predicts preference reversal

exchange economies and loss exposure experiments exchange economies were created in which individuals faced losses if people are risk seeking in the losses as predicted by prospect theory then due to the nonconvexity the competitive equilibria are all on the boundaries of the edgeworth box the experimental results are that risk seeking behavior is observed in many people and appears in markets as predicted in addition market behavior is consistent with answers to hypothetical questionnaires contrary to prospect theory risk seeking seems to diminish with experience preferences in the market setting are not labile and risk seeking preferences are not simply a result of framing effects copyright 1997 by american economic association

valuation optimal asset allocation and retirement incentives of pension plans we provide a framework in which we link the valuation and asset allocation policies of defined benefits plans with the lifetime marginal productivity schedule of the worker and the pension plan formula in turn we examine the retirement policies that are implied by the primitives of the model and the value of pension obligations our model provides an explicit valuation formula for a stylized defined benefits plan the optimal asset allocation policies consist of the replicating portfolio of the pension liabilities and the growth optimum portfolio independent of the pension liabilities we show that the worker will retire when the ratio of pension benefits to current wages reaches a critical value which depends on the parameters of the pension plan and the discount rate using numerical techniques we analyze the feedback effect of retirement policies on the valuation of plans and on the asset allocation decisions article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

willingness to pay and willingness to accept how much can they differ comment i agree with the point made by edoh y amiran and daniel a hagen 2003 that there can be a substantial or even infinite divergence between the wta and wtp for a public good even where there is a nonzero elasticity of substitution between market goods and the public good provided that the indifference curves are asymptotically bounded with respect to market goods in the manner they describe this is an important point they are also correct to point out that the elasticity of substitution is a local concept whereas their asymptotic boundedness condition applies also for discrete changes my 1991 paper used a local analysis because it was following the structure of the analysis in robert d willig 1976 and alan randall and john r stoll 1980 i wanted to show that while randall and stoll appeared to extend willig s local result on wta versus wtp from price changes to changes in the quantity of a public good the relevant elasticity was in fact different and involved the substitution elasticity as well as the income elasticity i view these points by amiran and hagen as not two separate results but essentially the same result their asymptotic boundedness condition generalizes my zero elasticity of substitution condition to discrete changes the asymptotic boundedness condition can be expressed as follows assuming a bivariate utility function u x q and given a reference point x q associated with a reference utility level u u x q there exists some q q such that for all q q there exists no x such that u x q u in other words no amount of x can substitute for the reduction in public good from q to q q in the case of a zero elasticity of substitution q q but as amiran and hagen show in their theorem 1 this is unnecessarily restrictive when dealing with a discrete reduction in q furthermore their theorem 2 can be viewed as a special case of their theorem 1 in which q 0 which makes q an essential commodity it is well known in consumer theory that the wta to avoid the loss of an essential market good is infinite their theorem 2 extends this result to the case of an essential nonmarket good but as their theorem 1 shows essentialness is not necessary for an infinite wta the boundedness condition is the key and this implies a fundamental lack of substitutability between money market goods and the public good

the shape of utility functions and organizational behavior based on measurements among 332 owner managers we investigate how theglobal shape of the utility function i e s shaped versus concave or convex over the total range of outcomes relates to choice behavior we find that the global shape of the utility function differs across decision makers about one third of the owner managers exhibit an s shaped utility function and that the global shape is linked to organizational behavior i e the production system employed a result that does not change when using different methods to identify the decision maker s global shape of the utility function the decision maker s risk attitude risk averse or risk seeking does not affect the choice of the production system whereas the degree of risk aversion based on thelocal shape of the utility function may be important in explaining owner managers trading behavior pennings and smidts 2000 more structural organizational behavior appears to be linked to theglobal shape of the utility function

optimal bank reorganization policies and the pricing of federal deposit insurance optimal dynamic regulatory policies for closing ailing banks and for deposit insurance premia are derived as functions of the rate of flow of bank deposits and interest rate on deposits the economy s risk free interest rate and the regulators bank audit administration costs under competitive conditions the threshold assets to deposits ratio below which a bank should be optimally closed is shown to be greater than or equal to one optimal deposit insurance premia and probabilities of bank closure are shown to be nondecreasing in the bank s risk on investment and nonincreasing in the bank s current assets to deposits ratio should regulatory agencies close reorganize an ailing federally insured financial institution if so when the recent record rate of failures of savings and loans associations s ls has renewed the urgency of this question the regulatory agencies are empowered but not required to reorganize financial institutions that are statutorily insolvent i e have zero or negative regulatory net worth recently regulators have in many instances permitted insolvent financial institutions to remain in operation 2 also while debating on the increase of the proposed funding of the federal deposit insurers the u s congress argued whether it would be desirable and if so when to close more s ls thus when regulators should close a troubled financial institution has become a major question of bank regulatory policy while the existing academic literature provides powerful insights into the structure and pricing of the insurers liability this literature offers very little guidance regarding the timing of bank reorganizations 3 indeed to the best of our knowledge the value of the federal

two economists musings on the stability of locus of control empirical studies of the role of non cognitive skills in driving economic behavior often rely heavily on the assumption that these skills are stable over the relevant time frame we analyze the change in a specific non cognitive skill i e locus of control in order to directly assess the validity of this assumption we find that short and medium run changes in locus of control are rather modest on average are concentrated among the young or very old do not appear to be related to the demographic labor market and health events that individuals experience and are unlikely to be economically meaningful still there is no evidence that locus of control is truly time invariant implying that the use of lagged measures results in an errors in variables problem that could downward bias the estimated wage return to locus of control by as much as 50 percent those researchers wishing to analyze the economic consequences of non cognitive skills should consider i restricting their analysis to the working age population for whom there is little evidence of systematic change in skill levels and ii accounting for error in the skill measures they employ

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

preference reversals the impact of truth revealing monetary incentives researchers vigorously debate the impact of incentives in preference reversal experiments do incentives alter behavior and generate economically consistent choices lichtenstein and slovic 1971 document inconsistencies reversals in revealed preference in gamble pairs across paired choice and individual pricing tasks the observed pattern is inconsistent with stable underlying preferences expressed with simple errors lichtenstein and slovic 1973 and grether and plott 1979 introduce incentives but aggregate reversal rates change little these results fostered numerous replications and assertions that models of non stable preferences are required to explain reversals contrary to this research we find that incentives can generate more economically consistent behavior our reevaluation of existing experimental data shows that incentives have a clear impact by better aligning aggregate choices and prices the effect is sufficiently large that with truth revealing incentives a stable preferences with error model not only explains behavior but fits the data as well as any model possibly could

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

loss aversion under prospect theory a parameter free measurement agrowing body of qualitative evidence shows that loss aversion a phenomenon formalized in prospect theory can explain a variety of field and experimental data quantifications of loss aversion are however hindered by the absence of a general preference based method to elicit the utility for gains and losses simultaneously this paper proposes such a method and uses it to measure loss aversion in an experimental study without making any parametric assumptions thus it is the first to obtain a parameter free elicitation of prospect theory s utility function on the whole domain our method also provides an efficient way to elicit utility midpoints which are important in axiomatizations of utility several definitions of loss aversion have been put forward in the literature according to most definitions we find strong evidence of loss aversion at both the aggregate and the individual level the degree of loss aversion varies with the definition used which underlines the need for a commonly accepted definition of loss aversion

estimating individual discount rates in denmark a field experiment we estimate individual discount rates with respect to time streams of money using controlled laboratory experiments these discount rates are elicited by means of field experiments involving real monetary rewards the experiments were carried out across denmark using a representative sample of 268 people between 19 and 75 years of age individual discount rates are estimated for various households differentiated by socio demographic characteristics such as income and age our conclusions are that discount rates are constant over the 12 month to 3 year horizons used in these experiments and that discount rates vary substantially with respect to several socio demographic variables hence we conclude that it would be reasonable to assume constant discount rates for specific household types but not the same rates across all households

consistency and heterogeneity of individual behavior under uncertainty by using graphical representations of simple portfolio choice problems we generate a very rich dataset to study behavior under uncertainty at the level of the individual subject we test the data for consistency with the maximization hypothesis and we estimate preferences using a two parameter utility function based on faruk gul 1991 this specification provides a good interpretation of the data at the individual level and can account for the highly heterogeneous behaviors observed in the laboratory the parameter estimates jointly describe attitudes toward risk and allow us to characterize the distribution of risk preferences in the population

venture theory a model of decision weights several theories suggest that people replace probabilities by decision weights when evaluating risky outcomes this paper proposes a model called venture theory of how people assess decision weights it is assumed that people first anchor on a stated probability and then adjust this by mentally simulating other possible values the amount of mental simulation is affected by the absolute size of payoffs the extent to which the anchor deviates from the extremes of 0 and 1 and the level of perceived ambiguity concerning the relevant probability the net effect of the adjustment i e up or down vis i vis the anchor reflects the relative weight given in imagination to values above as opposed to below the anchor this in turn is taken to be a function of both individual and situational variables and in particular the sign and size of payoffs cognitive and motivational factors therefore both play important roles in determining decision weights assuming that people evaluate outcomes by a prospect theory value function kahneman and tversky 1979 and are cautious in the face of risk fourteen predictions are derived concerning attitudes toward risk and ambiguity as functions of different levels of payoffs and probabilities the results of three experiments are reported whereas only a subset of the model s predictions can be tested in experiment 1 all fourteen are tested in experiments 2 and 3 using hypothetical and real payoffs respectively several of the model s predictions are not supported in experiment 2 but almost all are validated in experiments 1 and 3 the failures relate to the exact nature of probability payoff interactions in attitudes toward risk and ambiguity for losses the theory and results are discussed in relation to other experimental evidence future tests of the theory alternative models of risky choice and implications of venture theory for explaining further phenomena

ambiguity and nonparticipation the role of regulation we investigate the implications of ambiguity aversion for performance and regulation of markets in our model agents decision making may incorporate both risk and ambiguity and we demonstrate that nonparticipation arises from the rational decision by some traders to avoid ambiguity in equilibrium these participation decisions affect the equilibrium risk premium and distort market performance when viewed from the perspective of traditional asset pricing models we demonstrate how regulation particularly regulation of unlikely events can moderate the effects of ambiguity thereby increasing participation and generating welfare gains our analysis demonstrates how legal systems affect participation in financial markets through their influence on ambiguity the author 2009 published by oxford university press on behalf of the society for financial studies all rights reserved for permissions please e mail journals permissions oxfordjournals org oxford university press

the effects of imprecise probabilities and outcomes in evaluating investment options vagueness attitudes have been used to explain anomalies and irregularities in investment behavior it is generally assumed ellsberg 1961 that decision makers dms dislike vagueness but this assumption has been challenged by empirical results documenting systematic alternative attitudes to vagueness as a function of its source the domain of the decisions and the response mode used we investigate these three factors in a within subjects design that was embedded in an investment context dms evaluated investment options that varied in terms of their sources of vagueness probabilities and or outcomes in both domains gains or losses and employed two response modes pricing or choice we confirm that individuals vagueness attitudes are malleable contingent on the dimension salience and the reference domain in particular we observed three distinct patterns of reversals of attitudes towards vagueness our results indicate that the ability of vagueness attitudes to predict investment behavior is limited as decisions can be systematically influenced by task context and or perceived gain or loss positions economic models may be improved by incorporating more flexible assumptions about individuals attitudes toward vagueness