Local Expected Utility in Infinite-Dimensional Spaces: Theory and Elicitation

This paper develops a decision-theoretic interpretation of local expected utility on Abstract Wiener space. The framework is intended for economic acts that are naturally stochastic paths, such as income paths, consumption paths, investment payoffs, insurance losses, or laboratory stimuli unfolding over a continuum of contingencies. In this setting the object of choice is an act or payoff path, while Hermite functions serve as state-feature coordinates rather than objects of preference. Abstract Wiener space supplies a Gaussian reference measure on the Banach space of paths and a Hilbert subspace on which local utility is represented by orthogonal coefficients. The associated Wiener-integral weights are generally signed stochastic functionals; they become admissible decision weights only after a specified nonnegative normalization. This distinction clarifies the relation between the model, state-dependent utility, subjective expected utility, rank-dependent utility, and cumulative prospect theory. The main representation result gives finite primitive conditions under which projected path-valued acts admit a normalized local-utility representation. The corresponding elicitation result identifies composite utility-weight coefficients from projected acts and recovers normalized decision weights when the local utility scale is independently elicited. The paper also states testable restrictions: normalized weights must be nonnegative, add to one, preserve monotonicity, and satisfy additional rank or gain-loss restrictions when the subjective expected utility, rank-dependent utility, or cumulative prospect theory submodels are imposed. Numerical illustrations show how the representation operates in finite approximations.