arXiv 0903.22432009-03cs.ITmath.ITq-fin.PMq-fin.TR

务实信息率、凯利准则的推广及金融市场效率

Pragmatic Information Rates, Generalizations of the Kelly Criterion, and Financial Market Efficiency

Edward D. Weinberger

备注：: The fundamental formula for pragmatic information is true only in the special case where the a priori probabilities q(m) are average of the joint probabilities p(omega, m) over all incoming messages m. Also, the efficient market hypothesis (EMH) can still be true in a GARCH model, so the discussion of the EMH is confused

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AI总结：

本文探讨了务实信息率理论，将其应用于凯利准则推广和金融市场效率分析，揭示了市场无效的成因。

摘要：

本文是关于"务实信息"的持续研究的一部分，该定义在Weinberger（2002）中被定义为"在决策中实际使用的信息量"。由于信息率研究导致了无噪声和有噪声编码定理，这两个是香农理论中最重要结果，我们从定义务实信息率开始，证明所有相关极限都有意义，并将其解释为使用正确传输符号分布所获得的压缩改进。第一种应用将信息论分析扩展到凯利准则及其推广"赛马"，应用于一系列比赛中，其中获胜马匹、赔率和策略依赖于某些平稳过程，包括但不限于之前比赛的历史。如果赌徒接收到有关胜者概率分布的消息（侧信息），赌徒的 winnings 值的倍增率受这些消息的务实信息的限制。第二种应用是关于市场效率的问题。根据定义，有效市场是这样一个市场，其中"可交易的过去"相对于当前价格的务实信息为零。在这一定义下，具有GARCH（1，1）过程特征的市场不能有效。最后，香农无噪声编码定理的务实信息类比表明，市场无效的原因可能是基础资产变化太快，使得价格发现机制无法跟上。这可能在金融泡沫前夕最易发生，其中投资者的故意忽视会降低市场的信息处理能力。

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。