检验金融市场量子概率行为的实验设计
Design of an Experiment to Test Quantum Probabilistic Behavior of the Financial market
摘要：
最近的崩盘（再一次）表明，目前的金融数学对金融市场的描述不能完全令人满意。我们要提醒的是，如今的金融数学在很大程度上是基于随机变量和随机过程的使用，这些随机变量和随机过程由柯尔莫哥洛夫的概率测度理论模型（“经典概率模型”）描述。我推测，目前的金融危机是一个信号（一种测试古典概率论在金融市场有效性的实验），在金融中使用这个模型应该完全拒绝或至少完成。一个新的概率金融模型的最佳候选者之一是量子概率或其推广，也就是说量子（QL）模型。金融市场可能是非经典的猜测已经在科学文献中出现了很多年。本文的目的是从投机领域转向支持金融市场概率非经典性的严格统计论证。设计了一个基于违反全概率公式的统计检验。后者是经典概率的基础，它的违反将是一个强烈的迹象，有利于QL行为在市场上。
英文摘要：
The recent crash demonstrated (once again) that the description of the financial market by present financial mathematics cannot be considered as totally satisfactory. We remind that nowadays financial mathematics is heavily based on the use of random variables and stochastic processes which are described by Kolmogorov's measure-theoretic model for probability ("classical probabilistic model"). I speculate that the present financial crises is a sign (a kind of experiment to test validity of classical probability theory at the financial market) that the use of this model in finances should be either totally rejected or at least completed. One of the best candidates for a new probabilistic financial model is quantum probability or its generalizations, so to say quantum-like (QL) models. Speculations that the financial market may be nonclassical have been present in scientific literature for many years. The aim of this note is to move from the domain of speculation to rigorous statistical arguments in favor of probabilistic nonclassicality of the financial market. I design a corresponding statistical test which is based on violation of the formula of total probability (FTP). The latter is the basic in classical probability and its violation would be a strong sign in favor of QL behavior at 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。
