what are asset demand tests of expected utility really testing assuming the classic contingent claim setting a number of financial asset demand tests of expected utility have been developed and implemented in experimental settings however the domain of preferences of these asset demand tests differ from the mixture space of distributions assumed in the traditional binary lottery laboratory tests of von neumann morgenstern expected utility preferences we derive new sets axioms that are necessary and sufficient for preferences over contingent claims to be representable by an expected utility function we also indicate the additional axioms required to extend the representation to the more general case of preferences over risky prospects

recursive non expected utility connecting ambiguity attitudes to risk preferences and the level of ambiguity abstract i study how risk preferences and the level of ambiguity influence ambiguity attitudes in uzi segal s recursive second order non expected utility model it is shown that the negative certainty independence axiom for risk preferences is equivalent to a global form of ambiguity aversion that entails ambiguity averse behavior irrespective of the state space and the decision maker s second order belief thus the second order version of the cautious expected utility model is the only subclass of segal s theory that robustly predicts ambiguity aversion moreover a mean preserving spread operation over second order beliefs which corresponds to a particular way of increasing the level of ambiguity is equivalent to increasing the relative strength of ambiguity aversion for each possible specification of risk preferences within the cautious expected utility model an application of the latter result establishes a negative relation between participation rates in an asset market and the level of ambiguity concerning the distribution of returns

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

small worlds modeling attitudes toward sources of uncertainty abstract we introduce the concept of a conditional small world event domain an extension of savage s the foundations of statistics wiley new york 1954 notion of a small world as a self contained collection of comparable events under weak behavioral conditions we demonstrate probabilistic sophistication in any small world event domain without relying on monotonicity or continuity probabilistic sophistication within though not necessarily across small worlds provides a foundation for modeling a decision maker that has source dependent risk attitudes this also helps formalize the idea of source preference and suggests an interpretation of ambiguity aversion often associated with ellsberg type behavior in terms of comparative risk aversion across small worlds

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

dutch book arguments and learning in a nonexpected utility fremework if an individual follows maximin expected utility theory then a smart outsider cannot in general make a bet with him her that is certain to win in a single time period however the author shows that when there are many time periods this is possible in his model unless the decisionmaker uses strategic behavior there are some exceptions in particular for small deviations from expected utility profits may be less than the transactions costs copyright 1995 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

reduction of compound lotteries with objective probabilities theory and evidence abstract the reduction of compound lotteries axiom rocl has assumed a central role in the evaluation of behavior toward risk and uncertainty we present experimental evidence on its validity in the domain of objective probabilities our battery of lottery pairs includes simple one stage lotteries two stages compound lotteries and their actuarially equivalent one stage lotteries we find violations of rocl and that behavior is better characterized by a source dependent version of the rank dependent utility model rather than expected utility theory since we use the popular 1 in k random lottery incentive mechanism payment procedure in our main test our experiment explicitly recognizes the impact that this payment procedure may have on preferences thus we also collect data using the 1 in 1 payment procedure we do not infer any violations of rocl when subjects are only given one decision to make these results are supported by both structural estimation of latent preferences as well as non parametric analysis of choice patterns the random lottery incentive mechanism used as payment protocol itself induces an additional layer of compounding by design that might create confounds in tests of rocl therefore we provide a word of caution for experimenters interested in studying rocl for other purposes such as the relationship between ambiguity attitudes and attitudes toward compound lotteries to carefully think about the design to study rocl payment protocols and their interaction with the preferences being elicited

a dynamic ellsberg urn experiment two rationality arguments are used to justify the link between conditional and unconditional preferences in decision theory dynamic consistency and consequentialism dynamic consistency requires that ex ante contingent choices are respected by updated preferences consequentialism states that only those outcomes which are still possible can matter for updated preferences we test the descriptive validity of these rationality arguments with a dynamic version of ellsberg s three color experiment and find that subjects act more often in line with consequentialism than with dynamic consistency

is it inefficient investment that causes the diversification discount diversified conglomerates are valued less than matched portfolios of pure play firms recent studies find that this diversification discount results from conglomerates inefficient allocation of capital expenditures across divisions much of this work uses tobin s q as a proxy for investment opportunities therefore hypothesizing that q is a good proxy this paper treats measurement error in q using a measurement error consistent estimator on the sorts regressions in the literature i find no evidence of inefficient allocation of investment the results in the literature appear to be artifacts of measurement error and of the correlation between investment opportunities and liquidity diversif ied conglomerates appear to trade at a discount relative to matched portfolios of pure play firms studies documenting this stylized fact include lang and stulz 1994 berger and ofek 1995 comment and jarrell 1995 and servaes 1996 recent empirical work has sought to find the source of this diversification discount building on the theoretical work in milgrom and roberts 1990 stein 1997 and scharfstein and stein 2000 on the inefficiency of internal capital markets this literature has asked specifically whether diversified firms allocate their capital expenditures inefficiently across divisions the canonical answer has been yes and has been supported by two types of evidence first studies such as lamont 1997 shin and stulz 1998 shin and park 1998 and rajan servaes and zingales 2000 all find that internal capital markets in conglomerates transfer funds across divisions in a suboptimal manner second studies such as berger and ofek and scharfstein 1998 provide evidence suggesting that the divisions of conglomerates do not respond adequately to investment opportunities in comparison to single segment firms however these findings about divisional investment may be an artifact of measurement error most of these studies rely on tobin s q the market value of the capital stock divided by its replacement value as a proxy for investment opportunities and tobin s q is likely to be a poor proxy shin and stulz

eliciting subjective probabilities with binary lotteries abstract we evaluate a binary lottery procedure for inducing risk neutral behavior in a subjective belief elicitation task prior research has shown this procedure to robustly induce risk neutrality when subjects are given a single risk task defined over objective probabilities drawing a sample from the same subject population we find evidence that the binary lottery procedure also induces linear utility in a subjective probability elicitation task using the quadratic scoring rule we also show that the binary lottery procedure can induce direct revelation of subjective probabilities in subjects with popular non expected utility preference representations that satisfy weak conditions

a generalization of pratt arrow measure to nonexpected utility preferences and inseparable probability and utility 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

inducing risk neutral preferences with binary lotteries a reconsideration abstract we evaluate the binary lottery procedure for inducing risk neutral behavior we strip the experimental implementation down to bare bones taking care to avoid any potentially confounding assumptions about behavior having to be made in particular our evaluation does not rely on the assumed validity of any strategic equilibrium behavior or even the customary independence axiom we show that subjects sampled from our population are generally risk averse when lotteries are defined over monetary outcomes and that the binary lottery procedure does indeed induce a statistically significant shift toward risk neutrality this striking result generalizes to the case in which subjects make several lottery choices and one is selected for payment

a theory of subjective compound lotteries 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 that uncertainty aversion implies aversion to second order risk which implies issue preference and behavior consistent with the ellsberg paradox

a single stage approach to anscombe and aumann s expected utility anscombe and aumann showed that if one accepts the existence of a physical randomizing device such as a roulette wheel then savage s derivation of subjective expected utility can be considerably simplified they however invoked compound gambles to define their axioms we demonstrate that the subjective expected utility derivation can be further simplified and need not invoke compound gambles our simplification is obtained by closely following the steps by which probabilities and utilities are elicited

pareto optimal trade in an uncertain world gmos and the precautionary principle optimal trade policy in an uncertain world is examined decision maker attitudes toward uncertainty are represented in terms of the gilboa schmeidler 1989 maximin expected utility mmeu model the central result is that in a two country general equilibrium setting with both trading partners possessing an mmeu preference structure pareto optimality can require one trading partner to absorb all uncertainty in the economy if its set of priors is a subset of its trading partners an immediate corollary is that autarky is pareto optimal if the trading partner with the more inclusive set of priors either chooses or is endowed with a nonstochastic technology

quantile maximization in decision theory this paper introduces a model of preferences in which given beliefs about uncertain outcomes an individual evaluates an action by a quantile of the induced distribution the choice rule of quantile maximization unifies maxmin and maxmax as maximizing the lowest and the highest quantiles of beliefs distributions respectively and offers a family of less extreme preferences taking preferences over acts as a primitive we axiomatize quantile maximization in a savage setting our axiomatization also provides a novel derivation of subjective beliefs which demonstrates that neither the monotonicity nor the continuity conditions assumed in the literature are essential for probabilistic sophistication we characterize preferences of quantile maximizers towards downside risk we discuss how the distinct properties of the model robustness and ordinality can be useful in studying choice behaviour for categorical variables and in economic policy design we also offer applications to poll design and insurance problems

dual approaches to the analysis of risk aversion we present a dual formulation of choice under uncertainty based on a few simple assumptions about preferences it is shown that the additive separability restriction on preferences key to expected utility theory can be dropped with little loss of analytic power for a broad class of choice problems dual risk premiums are characterized and it is shown that placing various invariance restrictions on them leads naturally to generalizations of the concepts of cara crra and lrt familiar from expected utility theory each of these generalizations conforms to a notion of homotheticity

the rich domain of uncertainty source functions and their experimental implementation we often deal with uncertain events for which no probabilities are known several normative models have been proposed descriptive studies have usually been qualitative or they estimated ambiguity aversion through one single number this paper introduces the source method a tractable method for quantitatively analyzing uncertainty empirically the theoretical key is the distinction between different sources of uncertainty within which subjective choice based probabilities can still be defined source functions convert those subjective probabilities into willingness to bet we apply our method in an experiment where we do not commit to particular ambiguity attitudes but let the data speak

savage in the market we develop a behavioral axiomatic characterization of subjective expected utility seu under risk aversion given is an individual agent s behavior in the market assume a finite collection of asset purchases with corresponding prices we show that such behavior satisfies a revealed preference axiom if and only if there exists a seu model a subjective probability over states and a concave utility function over money that accounts for the given asset purchases

the possibility of speculative trade between dynamically consistent agents it is shown that interim dynamically consistent trade may be supported among agents who have resolute non consequential choice preferences

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

maxmin expected utility over savage acts with a set of priors abstract this paper provides an axiomatic foundation for a maxmin expected utility over a set of priors mmeu decision rule in an environment where the elements of choice are savage acts this characterization complements the original axiomatization of mmeu developed in a lottery acts or anscombe aumann framework by i gilboa and d schmeidler 1989 j math econ 18 141 153 mmeu preferences are of interest primarily because they provide a natural and tractable way of modeling decision makers who display an aversion to uncertainty or ambiguity the novel axioms are formulated using standard sequence techniques which allow cardinal properties of utility to be expressed directly through preferences journal of economic literature classification number d81

a multiechelon inventory model with fixed replenishment intervals this paper develops a new model for studying multiechelon inventory systems with stochastic demand for the model we assume that each site in the system orders at preset times according to an order up to policy that delivery times are deterministic and that the demand processes are stochastic with independent increments we introduce a new scheme for allocating stock in short supply which we call virtual allocation and which permits significant tractability we exercise the model on a set of test problems for two echelon systems to get insight into the structure of good policies the primary findings are that both the central warehouse upper echelon and the retail sites lower echelon should hold safety stock but that most of the safety stock should be at the retail sites consequently the central warehouse will stock out with high probability furthermore we show that the virtual allocation rule is near optimal for the set of test problems

ambiguity reasoned determination and climate change policy abstract this paper examines climate change benefit cost analysis in the presence of scientific uncertainty in the form of ambiguity the specific issue addressed is the robustness of benefit cost analyses of climate change policy alternatives to relaxation of savage s original axioms two alternatives to subjective expected utility seu are considered maximin expected utility meu and incomplete expected utility ieu among other results it is demonstrated that polar opposite recommendations can emerge in an ambiguous decision setting even if all agree on society s rate of time preference society s risk attitudes the degree of ambiguity faced and the scientific primitives we show that for a simple numerical simulation of our model an meu decision maker favors policies which immediately tackle climate change while an ieu decision prefers business as usual each agency shall assess the costs and benefits of the intended regulation and recognizing that some costs and benefits are difficult to quantify propose or adopt a regulation only upon a reasoned determination that the benefits of the intended regulation justify its cost executive order 12866 of the us president

choice under uncertainty with the best and worst in mind neo additive capacities the concept of a non extreme outcome additive capacity neo additive capacity is introduced neo additive capacities model optimistic and pessimistic attitudes towards uncertainty as observed in many experimental studies moreover neo additive capacities can be applied easily in economic problems as we demonstrate by examples this paper provides an axiomatisation of choquet expected utility with neo capacities in a framework of purely subjective uncertainty

ambiguity attitudes in a large representative sample using a theorem showing that matching probabilities of ambiguous events can capture ambiguity attitudes we introduce a tractable method for measuring ambiguity attitudes and apply it in a large representative sample in addition to ambiguity aversion we confirm an ambiguity component recently found in laboratory studies a insensitivity the tendency to treat subjective likelihoods as 50 50 thus overweighting extreme events our ambiguity measurements are associated with real economic decisions specifically a insensitivity is negatively related to stock market participation ambiguity aversion is also negatively related to stock market participation but only for subjects who perceive stock returns as highly ambiguous this paper was accepted by james smith decision analysis

ambiguity aversion with three or more outcomes abstract ambiguous choice problems which involve three or more outcome values can reveal aspects of ambiguity and ambiguity aversion which cannot be displayed in the classic two outcome ellsberg urn problems and hence are not always captured by models designed to accommodate them these aspects include allais type preferences over purely subjective acts attitudes toward different sources involving different amounts of ambiguity and attitudes toward ambiguity at different outcome levels this paper presents a few such examples and examines the standard models predictions and performance in such cases jel d81

risk sharing in the small and in the large abstract this paper analyzes risk sharing in economies with no aggregate uncertainty when agents have non convex preferences in particular agents need not be globally risk averse or uncertainty averse in the sense of schmeidler 1989 we identify a behavioral condition under which betting is inefficient i e every pareto efficient allocation provides full insurance and conversely if and only if agents supporting probabilities defined as in rigotti et al 2008 have a non empty intersection our condition is consistent with empirical and experimental evidence documenting violations of convexity in either outcomes or utilities our results show that the connection between speculative betting and inconsistent beliefs does not depend upon global notions of risk or ambiguity aversion

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

relative concave utility for risk and ambiguity this paper presents a general technique for comparing the concavity of different utility functions when probabilities need not be known it generalizes a yaari s comparisons of risk aversion by not requiring identical beliefs b kreps and porteus information timing preference by not requiring known probabilities c klibanoff marinacci and mukerji s smooth ambiguity aversion by not using subjective probabilities which are not directly observable and by not committing to violations of dynamic decision principles d comparative smooth ambiguity aversion by not requiring identical second order subjective probabilities our technique completely isolates the empirical meaning of utility it thus sheds new light on the descriptive appropriateness of utility to model risk and ambiguity attitudes

correlated nash equilibrium abstract we modify the epistemic conditions for nash equilibrium only to accommodate gilboa and schmeidler s i gilboa d schmeidler maxmin expected utility with nonunique prior j math econ 18 1989 141 153 maxmin expected utility preferences and identify the equilibrium concept in n player strategic games that characterizes the modified epistemic conditions the epistemic characterization supports the equilibrium concept as a minimal generalization of nash equilibrium in the sense that it deviates from nash equilibrium only in terms of players attitude towards ambiguity consequently comparing it with nash equilibrium constitutes a ceteris paribus study of the effects of ambiguity on how a game is played for example with ambiguity beliefs about action choices are in general correlated

a definition of uncertainty aversion a definition of uncertainty or ambiguity aversion is proposed it is argued that the definition is well suited to modelling within the savage as opposed to anscombe and aumann domain of acts the defined property of uncertainty aversion has intuitive empirical content behaves well in specific models of preference multiple priors and choquet expected utility and is tractable tractability is established through use of a novel notion of differentiability for utility functions called eventwise differentiability

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

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

a two parameter model of dispersion aversion the idea of representing choice under uncertainty as a trade off between mean returns and some measure of risk or uncertainty is fundamental to the analysis of investment decisions in this paper we show that preferences can be characterized in this way even in the absence of objective probabilities we develop a model of uncertainty averse preferences that is based on a mean and a measure of the dispersion of the state wise utility of an act the dispersion measure exhibits positive linear homogeneity sub additivity translation invariance and complementary symmetry since preferences are only weakly separable in terms of these two summary statistics the uncertainty premium need not be constant we generalize the concept of decreasing absolute risk aversion further we derive two fund separation and asset pricing results analogous to those that hold for the standard capm