Iterated Expectations under Cumulative Prospect Theory: an Impossibility Result
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 Cumulative Prospect Theory (CPT) when a decision maker has to choose between prospects that belong to a comonotonic class. Our conditions characterize the compatibility of a prominent alternative to expected utility with valuation methods that are commonly used in applied economics and finance, e.g. in binomial option pricing. The conditions can be viewed as an impossibility result.
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