Partial Law Invariance and Risk Measures
提出部分法则不变性，推广了决策理论和金融中常用的法则不变性与概率精炼，并完全刻画了部分法则不变的一致风险度量，给出了新风险度量类及其在不确定性下的风险评估应用。
We introduce partial law invariance, generalizing law invariance, and probabilistic sophistication widely used in decision theory, as well as statistical and financial applications. Partial law invariance may be interpreted as law invariance restricted to events for which there is no model uncertainty, reflecting practical situations in decision theory and financial risk management. We fully characterize partially law-invariant coherent risk measures via a novel representation formula. Strong partial law invariance is defined to bridge the gap between the above characterization and the classic representation formula of Kusuoka. We propose a few classes of new risk measures, including partially law-invariant versions of the expected shortfall and the entropic risk measures, and illustrate their applications in risk assessment under different types of uncertainty. We provide a tractable optimization formula for computing a class of partially law-invariant coherent risk measures and give a numerical example. This paper was accepted by Aurélien Baillon, behavioral economics and decision analysis. Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada [Grants CRC-2022-00141, RGPIN-2020-04356, and RGPIN-2024-03728]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2024.06518 .