Cumulative Prospect Theory for Parametric and Multiattribute Utilities

Different attitudes towards gains and losses are a prominent feature of cumulative prospect theory for decision under uncertainty. In particular, decision weights for uncertain events can depend on whether the events involve gains or losses, and the shape of the utility function can reveal loss aversion. Decision analyses concentrate on event capacities, which determine decision weights, and on the shape of the utility function. The present paper focuses on linear/exponential, power-function and multilinear utility models for decision under uncertainty. We begin with straightforward preference axioms for a representation by a cumulative prospect theory functional. The axioms include weak ordering, continuity, monotonicity and tail independence. We show that in their presence constant absolute (proportional) risk aversion implies linear/exponential (power) utility. Then, for the multiattribute case, (mutual) utility independence leads to a utility function that is (additive/multiplicative) multilinear.