无限维空间中的局部期望效用：理论与elicitation
Local Expected Utility in Infinite-Dimensional Spaces: Theory and Elicitation
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中文总结 AI 辅助
本文在抽象Wiener空间上为随机路径行为建立局部期望效用的决策论表示与elicitation方法，给出有限原始条件、权重归一化及可检验限制。
中文摘要 AI 辅助
本文在抽象Wiener空间上发展了局部期望效用的决策论解释。该框架旨在处理自然为随机路径的经济行为，例如收入路径、消费路径、投资回报、保险损失或在一系列偶然事件上展开的实验室刺激。在此设置中，选择对象是行为或回报路径，而Hermite函数作为状态特征坐标而非偏好对象。抽象Wiener空间在路径的Banach空间上提供高斯参考测度，以及一个Hilbert子空间，局部效用通过正交系数表示。相关的Wiener积分权重通常是有符号的随机泛函；只有在指定的非负归一化之后，它们才成为可接受的决策权重。这一区分澄清了模型、状态依赖效用、主观期望效用、等级依赖效用和累积前景理论之间的关系。主要表示结果给出了有限原始条件，在这些条件下，投影的路径值行为允许归一化局部效用表示。相应的elicitation结果从投影行为中识别复合效用权重系数，并在独立elicitation局部效用尺度时恢复归一化决策权重。论文还陈述了可检验的限制：归一化权重必须非负、总和为1、保持单调性，并在施加主观期望效用、等级依赖效用或累积前景理论子模型时满足额外的等级或得失限制。数值示例展示了该表示在有限近似中如何运作。
英文摘要
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.
