Iterated expectations under rank-dependent expected utility and implications for common valuation methods

This paper investigates the applicability of common valuation techniques in finance when the decision-maker's preferences can be described by the rank-dependent expected utility model. Under expected utility theory, compound lotteries can be valued by "iterating" expectations: the expected utility of a compound lottery is the expected value of a simple lottery over prizes that are certainty equivalents to follow-up lotteries. We derive necessary and sufficient conditions for a similar valuation technique in the framework of rank-dependent expected utility when a consequentialist decision-maker has to choose between prospects that belong to a comonotonic class. The conditions coincide with those for dynamically consistent behaviour of such a decision-maker. The decision-maker must update her preferences based on a benchmark prospect that can be interpreted as a formalization of "black-and-white thinking."