实用信息、计算与有效市场假说
Pragmatic Information, Computation, and the Efficient Market Hypothesis
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中文总结 AI 辅助
该研究针对标准信息理论的意义度量缺口，提出实用信息概念，结合乔姆斯基层级与计算能力分析，将有效市场假说重构为参与者特定的计算效率，认为计算资源差异导致市场效率认知分化且持续存在。
中文摘要 AI 辅助
我们解决了标准信息理论中一个长期存在的缺口，即该理论无法对传输消息中的意义量赋予度量。Weinberger等人（2024）提出了一种特定的意义定量度量，将其称为实用信息，具备该度量应有的诸多特性。随后我们证明，给定接收器可从某消息中提取的实用信息量取决于接收器的计算能力，尤其是其识别形式语言乔姆斯基层级中不同复杂度层级符号串的能力。某一符号串对特定接收器而言可能看似完全随机，但对层级中更高层级的接收器则不然；因此，即便层级中对应层级的另一接收器可从该串中提取实用信息，此接收器也可能无法提取任何实用信息。此外，不同复杂度层级消息的最大处理速率可作为一种实用信道容量，导致提取的实用信息量与提取时间之间存在权衡。我们随后将定量金融中的有效市场假说重新表述为参与者特定的“计算效率”，即主张参与者缺乏利用可用实用信息“跑赢市场”所需的计算资源。鉴于市场参与者的计算资源差异巨大，因此部分参与者会认为某一市场具有计算效率，即便其他参与者发现了市场低效，这也不足为奇。我们认为，即便面对任何可想象的计算能力提升，这种情况也将持续存在。
英文摘要
The efficient market hypothesis, that prices reflect all available information, imputes a meaning to market moving information, a view of information foreign to standard information theory. Here, after reviewing properties that make a proposed formula for ``pragmatic information" a plausible measure of meaning, we consider the role that the receiver's position in the machine hierarchy corresponding to the Chomsky hierarchy play in extracting this meaning. We show that a receiver at a given level in the hierarchy may be unable to extract pragmatic information from a message because it appears random, yet a receiver at a higher level in the hierarchy finds the message perfectly intelligible. Also, the maximum processing rates for messages of different levels of hierarchy serve as a kind of channel capacity, leading to a tradeoff between the amount of pragmatic information extracted and the extraction time. All of the above suggests a recasting of market efficiency in terms of ``computational efficiency'', i.e. the question of whether a market appears efficient to a participant with a given computational endowment. Successful trading strategies implementable as finite state machines, the lowest level in the hierarchy, imply departures from ``finite state efficiency''. We show, via a stylized example, how pragmatic information can characterize the ensuing approach to finite state efficiency. We also show that actual market dynamics can be more computationally intractable than any finite state machine can process by proving the PSPACE-completeness of the processing of the smart order routing systems of major brokerage firms. We conclude that computational efficiency is the norm and pragmatic information can characterize any departure from it.
发表机构
- NYU Tandon School of Engineering（纽约大学坦登工程学院）
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