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A second-generation disappointment aversion theory of decision making under risk

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Abstract

This paper presents a new decision theory for modelling choice under risk. The new theory is a two-parameter generalization of expected utility theory. The proposed theory assumes that a decision maker: (1) behaves as if maximizing expected utility; but (2) may experience disappointment (elation) when the utility of a lottery’s outcome falls short of (exceeds) the expected utility of the lottery; and (3) may have a preference for gambling (attraction/aversion to positively/negatively skewed lotteries). The proposed theory can rationalize the fourfold pattern of risk attitudes; the common ratio effect and the reverse thereof (in certain types of decision problems); the Allais paradox in classical common consequence problems and the reverse Allais paradox—in common consequence problems with an even split of a probability mass; violations of the betweenness axiom; switching behavior in the Samuelson’s example; violations of ordinal, upper and lower cumulative independence (which falsify rank-dependent utility and cumulative prospect theory); and preference reversals between valuations and choice. In application to insurance, the theory can rationalize full insurance with an actuarially unfair premium and aversion to probabilistic insurance. In application to optimal portfolio investment, the theory can rationalize the equity premium puzzle.

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Notes

  1. In particular, the models proposed by Bell (1985), Loomes and Sugden (1986) and Jia et al. (2001) cf. Sect. 6 below.

  2. I.e. risk aversion for probable gains or improbable losses and risk seeking for improbable gains or probable losses.

  3. Quiggin (1981) rank-dependent utility or Tversky and Kahneman (1992) cumulative prospect theory with a popular probability weighting function \(w( p )=p^{\gamma }/({p^{\gamma }+({1-p})^{\gamma }})^{1/\gamma }\) shares the same limitation.

  4. A simultaneous combination of quasi-concave and quasi-convex preferences (Bernasconi 1994).

  5. In other words, cumulative probability \(1-0.01x\) is uniformly distributed over interval [x, 100].

  6. Markowitz (1952, p. 90) noted that the third moment “may be connected with a propensity to gamble”.

  7. This cubic probability weighting function \(w( p )=p-\rho \cdot p( {1-p} )+\tau \cdot p( {1-p} )( {1-2p} )\) is analyzed in Blavatskyy (2016).

  8. Many studies find that decision making under risk is a probabilistic rather than a deterministic process. For example, Camerer (1989, p. 81), Hey and Orme (1994, p. 1296) as well as Ballinger and Wilcox (1997, p. 1100) found that 31.6, 25 and 20.8% of subjects respectively reverse their choice when presented with the same decision problem within a short period of time.

  9. Restriction to four outcomes is a common approach in experimental economics to facilitate a non-parametric estimation of a Bernoulli utility function (e.g., Hey and Orme 1994; Hey 2001).

  10. The rule of thumb is the following: (1) choose a lottery with the lowest probability of the worst possible outcome; (2) if both lotteries yield the same probability of the worst possible outcome then choose the lottery with the highest probability of the best possible outcome.

  11. E.g. when comparing expected utility theory and the maximization of expected value.

  12. If two or more theories are not significantly different in terms of goodness of fit, then only a theory with fewer subjective parameters is shown on Fig. 5.

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  1. Montpellier Business School, Montpellier Research in Management, 2300, Avenue des Moulins, 34185, Montpellier Cedex 4, France

    Pavlo Blavatskyy

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Blavatskyy, P. A second-generation disappointment aversion theory of decision making under risk. Theory Decis 84, 29–60 (2018). https://doi.org/10.1007/s11238-017-9629-5

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