We propose and characterize a model of preferences over acts such that the decision maker prefers act f to act g if and only if E μ φ( E π u○f) ⩾ E μ φ( E π u○g), where E is the expectation operator, u is a von Neumann-Morgenstern utility function, φis an increasing transformation, and μis a subjective probability over the set Πof probability measures πthat the decision maker thinks are relevant given his subjective information. A key feature of our model is that it achieves a separation between ambiguity, identified as a characteristic of the decision maker's subjective beliefs, and ambiguity attitude, a characteristic of the decision maker's tastes. We show that attitudes toward pure risk are characterized by the shape of u, as usual, while attitudes toward ambiguity are characterized by the shape of φ. Ambiguity itself is defined behaviorally and is shown to be characterized by properties of the subjective set of measures Π. One advantage of this model is that the well-developed machinery for dealing with risk attitudes can be applied as well to ambiguity attitudes. The model is also distinct from many in the literature on ambiguity in that it allows smooth, rather than kinked, indifference curves. This leads to different behavior and improved tractability, while still sharing the main features (e.g., Ellsberg's paradox). The maxmin expected utility model (e.g., Gilboa and Schmeidler (1989)) with a given set of measures may be seen as a limiting case of our model with infinite ambiguity aversion. Two illustrative portfolio choice examples are offered. Copyright The Econometric Society 2005.
for helpful discussion, Andreas Lange for pointing out an error in a previous version and seminar audiences at the Cowles Foundation workshop "Uncertainty in Economic Theory,"the
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 behavior. This paper uses ambiguity aversion to understand aspects of behavior of financial markets. More particularly, the paper focuses on the question, "What prevents the typical bond-equity finance economy from offering sufficient opportunities for Pareto optimal risk sharing? In other words, why should the theorems of general equilibrium with incomplete markets (GEI), rather than general equilibrium with complete markets (GE), be a more compelling description of the typical bond-equity economy?" To analyze the question, we consider a stylized bond-equity economy, which though incomplete per se, has a rich enough set of assets available for trade such that given standard assumptions about behavior under uncertainty, the equilibrium allocation would arbitrarily approximate a complete market (GE) allocation. We show, however, that given 'sufficient' ambiguity aversion, a certain subset of the available assets will not be actually traded in equilibrium, even though available. Hence it is proved that, given 'sufficient' ambiguity aversion, provided the non-traded securities are non-redundant, equilibrium allocation of the bond-equity economy is a GEI equilibrium. Thus we show how ambiguity aversion may endogenously limit the scope of risk sharing obtainable through the bonds/equities actually traded in a typical economy, and therefore, explain why the actual behavior of such an economy is better described by the GEI model, rather than the GE model. The formal analysis in this paper basically involves a reconsideration of the general equilibrium of a simple 'finance economy' while allowing for ambiguity aversion. The underlying objective is to identify the class of assets whose trade is vulnerable to ambiguity aversion: assets that will be traded if agents are subjective expected utility maximizers but not if the agents' common beliefs about payoffs of the assets is sufficiently ambiguous and the agents are ambiguity averse. We find that what determines an asset's vulnerability to ambiguity aversion is whether its payoffs have an idiosyncratic component, i.e., if at least some component of the payoff is independent of the realized endowment vector and of the payoff of any other asset as well. It turns out that if, (1) the range of variation of the payoff's idiosyncratic component is 'large' relative to the range of the variation of the component correlated with the endowment vector and, (2) the ambiguity of the agents' common belief about the idiosyncratic component is sufficiently high, then the asset will not be tra...
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 paper shows that this argument is not robust: 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.
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