Abstract This paper provides a theoretical analysis on the impacts of using a suboptimal information set for the estimation of the pricing kernel and, more in general, for the validity of the fundamental theorems of asset pricing. While inferring the risk-neutral measure from options data provides a naturally forward-looking estimate, extracting the real world measure from historical returns is only partially informative, thus suboptimal with respect to investors’ future beliefs. As a consequence of this disalignment, the two measures no longer share the same nullset, thus distorting the investors’ risk premium and the validity of the pricing measure. From a probabilistic viewpoint, the missing beliefs are totally unaccessible stopping times on the coarser filtration set, so that an absolutely continuous strict local martingale, once projected on it, becomes continuous with jumps. Some empirical examples complete the paper.

中文翻译：

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情绪损失：将定价内核投影到较小的过滤集上的效果

摘要 本文对使用次优信息集对定价核估计的影响进行了理论分析，更一般地说，对资产定价基本定理的有效性进行了理论分析。虽然从期权数据中推断风险中性度量提供了自然的前瞻性估计，但从历史回报中提取现实世界的度量仅提供部分信息，因此对于投资者的未来信念而言是次优的。由于这种不一致，这两种度量不再共享相同的零集，从而扭曲了投资者的风险溢价和定价度量的有效性。从概率的角度来看，缺失的信念是在较粗的过滤集上完全无法访问的停止时间，因此绝对连续的严格局部鞅，一旦投射到它上面，就会随着跳跃变得连续。一些实证例子完成了这篇论文。