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摘要翻译：
本文是正在进行的“语用信息”研究的一部分，“语用信息”在Weinberger(2002)中被定义为“决策中实际使用的信息量”。由于对信息率的研究导致了无噪声编码定理和有噪声编码定理，这是香农理论的两个最重要的结果，我们首先定义了一个实用信息率，表明所有相关的限制都是有意义的，并将它们解释为使用正确的传输符号分布而获得的压缩改进。该理论的两个应用中的第一个将凯利准则及其推广的信息论分析扩展到一系列比赛，其中获胜的马、收益和策略的随机过程依赖于某种平稳过程，包括但不限于以前比赛的历史。如果投注者正在接收关于获胜者概率分布的消息（边信息），则投注者奖金的翻倍率受消息的语用信息的限制。第二个应用是市场效率问题。根据定义，一个有效的市场是这样一个市场，在这个市场中，关于当前价格的“可交易的过去”的实用信息为零。在这个定义下，收益率以GARCH(1,1）过程为特征的市场不可能是有效的。最后，对香农噪声编码定理的一个实用的信息类比表明，市场无效的一个原因是潜在的基本面变化如此之快，以至于价格发现机制根本跟不上。这种情况最容易发生在金融泡沫的前夕，投资者的故意无知削弱了市场的信息处理能力。
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英文标题：
《Pragmatic Information Rates, Generalizations of the Kelly Criterion, and
Financial Market Efficiency》
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作者：
Edward D. Weinberger
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最新提交年份：
2014
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分类信息：
一级分类：Computer Science 计算机科学
二级分类：Information Theory 信息论
分类描述：Covers theoretical and experimental aspects of information theory and coding. Includes material in ACM Subject Class E.4 and intersects with H.1.1.
涵盖信息论和编码的理论和实验方面。包括ACM学科类E.4中的材料，并与H.1.1有交集。
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一级分类：Mathematics 数学
二级分类：Information Theory 信息论
分类描述：math.IT is an alias for cs.IT. Covers theoretical and experimental aspects of information theory and coding.
它是cs.it的别名。涵盖信息论和编码的理论和实验方面。
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一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Quantitative Finance 数量金融学
二级分类：Trading and Market Microstructure 交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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英文摘要：
This paper is part of an ongoing investigation of "pragmatic information", defined in Weinberger (2002) as "the amount of information actually used in making a decision". Because a study of information rates led to the Noiseless and Noisy Coding Theorems, two of the most important results of Shannon's theory, we begin the paper by defining a pragmatic information rate, showing that all of the relevant limits make sense, and interpreting them as the improvement in compression obtained from using the correct distribution of transmitted symbols. The first of two applications of the theory extends the information theoretic analysis of the Kelly Criterion, and its generalization, the horse race, to a series of races where the stochastic process of winning horses, payoffs, and strategies depend on some stationary process, including, but not limited to the history of previous races. If the bettor is receiving messages (side information) about the probability distribution of winners, the doubling rate of the bettor's winnings is bounded by the pragmatic information of the messages. A second application is to the question of market efficiency. An efficient market is, by definition, a market in which the pragmatic information of the "tradable past" with respect to current prices is zero. Under this definition, markets whose returns are characterized by a GARCH(1,1) process cannot be efficient. Finally, a pragmatic informational analogue to Shannon's Noisy Coding Theorem suggests that a cause of market inefficiency is that the underlying fundamentals are changing so fast that the price discovery mechanism simply cannot keep up. This may happen most readily in the run-up to a financial bubble, where investors' willful ignorance degrade the information processing capabilities of the market.
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PDF链接：
https://arxiv.org/pdf/0903.2243
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