Behavioral premium principles

We define a premium principle under the continuous cumulative prospect theory which extends the equivalent utility principle. In prospect theory, risk attitude and loss aversion are shaped via a value function, whereas a transformation of objective probabilities, which is commonly referred as probability weighting, models probabilistic risk perception. In cumulative prospect theory, probabilities of individual outcomes are replaced by decision weights, which are differences in transformed, through the weighting function, counter-cumulative probabilities of gains and cumulative probabilities of losses, with outcomes ordered from worst to best. Empirical evidence suggests a typical inverse-S shaped function: decision makers tend to overweight small probabilities, and underweight medium and high probabilities; moreover, the probability weighting function is initially concave and then convex. We study some properties of the behavioral premium principle. We also assume an alternative framing of the outcomes; then, we discuss several applications to the pricing of insurance contracts, considering different value functions and probability weighting functions proposed in the literature, and an alternative mental accounting. Finally, we focus on the shape of the probability weighting function.