适应律不变性与时间一致的动态风险度量
Adapted Law Invariance and Time-Consistent Dynamic Risk Measures
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中文总结 AI 辅助
研究动态风险度量中适应律不变性，证明其与递归一步条件律表示等价，给出动态风险度量的构建方式，刻画其凸性和连贯性，还得到适应的Kusuoka表示并扩展了相关定理。
中文摘要 AI 辅助
在静态风险度量中，律不变性表明头寸风险仅取决于其分布。在动态环境中，自然引出适应律不变性，即风险评估应仅取决于金融头寸的概率结构及其随时间的信息揭示方式。我们表明，对于时间一致的风险度量，适应律不变性等同于递归一步条件律表示。
英文摘要
In static risk measurement, law invariance expresses the principle that the risk of a position should depend only on its distribution, and not on the particular probability space on which it is represented. In a dynamic setting, the same principle leads naturally to adapted law invariance: the risk assessment should depend only on the probabilistic structure of the financial position together with the way information about it is revealed over time. We show that, for time-consistent risk measures, adapted law invariance is equivalent to a recursive one-step conditional-law representation. More precisely, assuming Fatou regularity, the one-step risk evaluations are exactly conditional lifts of static law-invariant risk measures, and the full dynamic risk measure is obtained by backward composition of these one-step maps. Convexity and coherence of the dynamic risk measure are characterized by the corresponding properties of the static one-step risk measures. This identifies adapted law invariance as the dynamic counterpart of ordinary law invariance. It also clarifies the strength of terminal-law invariance, as it appears in the rigidity theorem of Kupper and Schachermayer: it does not distinguish risks with the same distribution but different times of resolution. We further obtain an adapted Kusuoka representation in the coherent case and establish an extension of the Kupper--Schachermayer theorem.
