Cumulative prospect theory for parametric and multiattribute utilities

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