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Great Expectations: Prospect Theory with a Consistent Reference Point

This paper introduces a prospect theory model of risk preferences with an endogenously determined expectation that serves simultaneously as both the reference point for and the certainty equivalent of a lottery. This model accommodates a number of psychologically motivated and empirically observed risk preferences. We show that an agent can always form a consistent expectation for any gamble and derive a parametric formula for binary gambles, which can then be used to examine the effects of loss aversion, risk aversion, and probability weighting on behavior under risk. To illustrate the applicability of the results, we use this model to consider the incentives of an agent purchasing insurance against the possibility of a loss and show that it is optimal for him to either purchase full insurance or purchase no insurance.