In decision theory and economics, ambiguity aversion (also known as uncertainty aversion) describes an attitude of preference for known risks over unknown risks. People would rather choose an option with fewer unknown elements than with many unknown elements. It is demonstrated in the Ellsberg paradox (i.e. that people prefer to bet on an urn with 50 red and 50 blue balls, than in one with 100 total balls but where the number of blue or red balls is unknown). There are a number of choices involving uncertainty and normally they can be classified in two categories: risky and ambiguous events. Risky events have a certain probability for a given outcome. Ambiguous events have a much greater degree of uncertainty. This includes the uncertainty of outcome and also the probability of an event occurring or the payoff associated with such events. The reaction is behavioral and still being formalized. Ambiguity aversion can be used to explain incomplete contracts, volatility in stock markets, and selective abstention in elections (Ghirardato & Marinacci, 2001)
The distinction between ambiguity aversion and risk aversion is important but subtle. Risk aversion comes from a situation where a probability can be assigned to each possible outcome of a situation. Ambiguity aversion applies to a situation when the probabilities of outcomes are unknown (Epstein 1999). The main idea behind ambiguity aversion encompasses the idea of risk aversion. A real world consequence of increased ambiguity aversion is the increased demand for insurance because the general public are averse to the unknown events that will affect their lives and property (Alary, Treich, and Gollier 2010).
Ambiguity aversion is a person’s rational attitude towards the probability of future outcomes, both unfavorable and favorable. People who are “ambiguity inverse” will increase the probability of the unfavorable prospect. Ambiguity aversion has been widely observed in individuals judgments, especially when it comes to pairs of individuals. There are both risky and cautious shifts that can take place between individuals’ original judgements and current judgments and ambiguity aversion investigates those reasons.
Women are more risk averse than men. One potential explanation for gender differences is that risk and ambiguity are related to cognitive and noncognitive traits on which men and women differ. Women initially respond to ambiguity much more favorably than men, but as ambiguity increases, men and women show similar marginal valuations of ambiguity. Psychological traits are strongly associated with risk but not to ambiguity. Adjusting for psychological traits explains why a gender difference exists within risk aversion and why these differences are not a part of ambiguity aversion. Since psychological measures are related to risk but not to ambiguity, risk aversion and ambiguity aversion are distinct traits because they depend on different variables (Borghans, Golsteyn, Heckman, Meijers.)
Smooth ambiguity preferences are represented as:
Real option valuation has traditionally been concerned with investment under project value uncertainty while assuming the agent has perfect confidence in a specific model. (Jaimungal) The classical model of McDonald and Siegel developed quantitative methods used to analyze the options. They investigate the problem from the approach of derivative pricing and assign the value of the option to invest as The expected value is taken under an appropriate risk-adjusted measure, I is the cost of investing in the project, Pt is the value of the project at time t and T denotes the family of allowed stopping times in [0; T ]. In the European case, the agent may invest in the project only at maturity, in the Bermudan case, the agent may invest at a set of specific times (e.g. monthly), and in the American case, the agent may invest at any time. As such, the problem is in general a free boundary problem in which the optimal strategy is computed simultaneously with the option's value. (Jaimungal)
Note that it is not the same as risk aversion, since it is a rejection of types of risk based in part on measures of their certainty, not solely on their magnitude.