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Decision theory

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)

## Contents

- 1 Ambiguity aversion vs. risk aversion
- 2 Measurements of ambiguity aversion
- 3 Gender difference in ambiguity aversion
- 4 A framework that allows for ambiguity preferences
- 5 An examination of ambiguity aversion: Are two heads better than one?
- 6 Ambiguity aversion in real options
- 7 See also
- 8 References

## Ambiguity aversion vs. risk aversion[edit | edit source]

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).

## Measurements of ambiguity aversion[edit | edit source]

Ambiguity aversion is a person’s rational attitude towards the probability of future outcomes, both unfavorable and favorable. People who are “ambiguity averse” 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.

## Gender difference in ambiguity aversion[edit | edit source]

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.)

## A framework that allows for ambiguity preferences[edit | edit source]

Smooth ambiguity preferences are represented as:

- s ∈ S set of contingencies or states
- πθ is a probability distribution over S
- f is an “act” yielding state contingent payoffs f (s)
- u is a von Neumann-Morgenstern utility function and represents risk attitude
- φ maps expected utilities and represents ambiguity attitude
- Ambiguity attitude is summarized using measure similar to absolute risk aversion, only absolute ambiguity aversion:
- μ is a subjective probability over θ ∈ Θ; Represents the ambiguous belief – it summarizes the decision-maker’s subjective uncertainty about the “true” πθ, probability distribution over contingencies. (Collar, 2008)

## An examination of ambiguity aversion: Are two heads better than one?[edit | edit source]

- Ambiguity aversion has been widely observed in individuals' judgments. The experiment examines risky and cautious shifts from individuals' original judgments to their judgments when they are paired up in dyads.
- In the experiment the participants were first asked to specify individually their willingness-to-pay for six monetary gambles. They were then paired at random into dyads, and were asked to specify their willingness-to-pay amount for the same gambles. The dyad's willingness-to-pay amount was to be shared equally by the two individuals. Of the six gambles in our experiment, one involved no ambiguity and the remaining five involved different degrees of ambiguity. It is found that dyads exhibited risk aversion as well as ambiguity aversion. The majority of the dyads exhibited a cautious shift in the face of ambiguity, stating a smaller willingness-to-pay than the two individuals' average.
- People pay less under ambiguous situations when compared to a corresponding unambiguous situation (Scenario 2 vs. Scenario 1). Similarly, they pay less for more ambiguous situations as compared to less ambiguous situations (Scenarios 4 vs. 3 and 6 vs. 5).

## Ambiguity aversion in real options[edit | edit source]

Real option valuation has traditionally been concerned with investment under project value uncertainty while assuming the agent has perfect confidence in a specific model.^{[1]} 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.

## See also[edit | edit source]

- Ambiguity tolerance
- Choquet expected utility
- David Schmeidler
- Knightian uncertainty
- Precautionary principle
- Uncertainty

## References[edit | edit source]

- ↑ Jaimungal, (2011) Irreversible Investments and Ambiguity Aversion, http://ssrn.com/abstract=1961786

- Schmeidler, David (May 1989). Subjective Probability and Expected Utility without Additivity.
*Econometrica***57**(3): 571–587. - Epstein, Larry G. (July 1999). A Definition of Uncertainty Aversion.
*The Review of Economic Studies***66**(3): 579.\\ - Alary, D., Gollier, C. G., & Treich, N. (2010, March 15). The eﬀect of ambiguity aversion on risk reduction and insurance demand. Retrieved from http://www.economics.unsw.edu.au/contribute2/Economics/news/documents/NicolasApri10.pdf
- Borghanst, L., Golstey, B. H. H., Heckman, J. J., & Meijer, H. (2009, January). Gender differences in risk aversion and ambiguity aversion. Retrieved from http://ftp.iza.org/dp3985.pdf

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