Simone Cerreia-Vioglio, Fabio Maccheroni and Massimo Marinacci (Department of Decision Sciences) with Luigi Montrucchio (Università di Torino), in their Uncertainty Averse Preferences (Journal of Economic Theory, Vol. 146, Issue 4, July 2011, pages 1275-1330, doi: 10.1016/j.jet.2011.05.006), propose a model which unifies existing models of decision under uncertainty displaying uncertainty aversion. The authors argue that these models differ in the specification of an uncertainty aversion index they suggest.
Every day individuals make choices with uncertain outcomes. Financial choices are an obvious example. Uncertainty is better understood if categorized into two types: risk and Knightian uncertainty. Risk refers to situations in which the likelihood of the outcomes of a choice is known and uncertainty is thereof measurable. A bet at the roulette is a simple case of this kind of uncertainty. On the other hand, the term Knightian uncertainty refers to a source of uncertainty which is not fully understood by the decision maker and isn’t thereof measurable by probability. This translates into the absence of a probability distribution governing the results. A bet on a horse race is the clearest example of this kind of uncertainty.
Economists have traditionally focused on situations of choice under risk. But the study of circumstances of choice under Knightian uncertainty (henceforth, uncertainty) has played an important role in recent decision theory and in its financial and economic applications. The point is that most of economic choices are made under conditions of uncertainty. Moreover, theories dealing just with risk turned out to be unable to explain important economic and financial facts such as the equity premium puzzle. The problem with the equity premium puzzle is that if decision makers knew the actual probability distribution of equity returns, their choices and the higher returns of equity over government bonds would be caused by a degree of risk aversion which data do not support. Some scholars, then, have suggested that these abnormal extra-returns could be the result of uncertainty aversion, i.e. the aversion to ignorance of the likelihood of events on equity markets.
In the last quarter of century, many decision criteria have been suggested and axiomatized in order to explain the behaviour of individuals under uncertainty. A large number of these criteria share two pivotal hypotheses: monotonicity (preference for better consequences in any state of the world) and uncertainty aversion (attitude to diversify). Anyway we still lack a common model to explain the existing ones as belonging to a single, large class of models. Cerreia-Vioglio, Maccheroni, Marinacci and Montrucchio provide such a model. The authors show that preferences displaying monotonicity and uncertainty aversion fit into a decision criterion based on an uncertainty aversion index, a risk aversion index and a pessimistic aggregation rule. Furthermore, their work highlights that any model developed in the past satisfying the aforementioned hypotheses corresponds to a definite specification of the uncertainty index the authors propose.