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Partially Law-Invariant Risk Measures

Yi ShenZachary Van OostenRuodu Wang
Jan 2024
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摘要原文
We introduce the concept of partial law invariance, generalizing the concept of law-invariant risk measures widely used in statistical and financial applications. This new concept is motivated by practical considerations of decision-making under uncertainty, thus connecting the literature on decision theory and that on financial risk management. We fully characterize partially law-invariant coherent risk measures via a novel representation formula, which, surprisingly, has little resemblance to the classical formula for law-invariant coherent risk measures. A notion of strong partial law invariance is introduced, allowing for a representation formula akin to the classical one. 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 model uncertainty.
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