负概率在经济学中的应用

Curca Sorin-Nicolae
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摘要

“负概率”的概念已成为研究的热点之一。最初是在物理学中发展起来的(负概率在量子现象的分析中很重要),现在它在许多其他科学学科中都有应用。它的主要优点是它扩展了经典的概率论,它涉及0到1之间的值,允许负的或超酉的值。从这个角度来看,负概率是一个有用的工具,可以方便计算,并通过模型使分析更加灵活。本文旨在提出理论框架,一般来说,可以理解经济学中负概率的使用与之相关的原则。现有文献强调负概率在随机过程的分析中是合适的,并且从这个角度来看,已经开发了应用,特别是在金融领域。从这个意义上讲,负概率用于诸如二项CRR模型(Cox-Ross-Rubinstein市场模型)之类的模型,该模型用于评估资本市场上衍生品的价格,包括隐藏变量(不可观察)等。在我们的分析中,我们描述了这些模型,并在此基础上,我们试图确定可用于经济领域的负概率的特征。这项研究是一项理论研究,为在宏观经济建模中使用负概率的新方法开辟了道路。
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THE USE OF NEGATIVE PROBABILITIES IN ECONOMICS
The concept of „negative probability” has become one of interest in research. Initially developed in connection with physics (negative probabilities are important in the analysis of quantum phenomena), nowadays it has applications in many other scientific disciplines. Its main advantage is that it extends the classical probability theory, which involves values between 0 and 1, allowing negative or supraunitary values. From this point of view, negative probabilities are a useful tool that facilitates the calculation and makes analysis more flexible through models. This paper aims to present the theoretical framework, the principles in relation to which the use of negative probabilities in economics, in general, can be understood. The existing literature highlights that the negative probabilities are appropriate in the analysis of stochastic processes and, from this perspective, has developed applications especially in the field of finance. In this sense, negative probabilities are used in models such as the binomial CRR model (The Cox-Ross-Rubinstein Market Model), that evaluate the price of derivatives on the capital market, those that include hidden variable (non-observable) etc. In our analysis we describe these models and, based on them, we try to identify the features of the negative probabilities that can be used in the economic field. The research is a theoretical one, leading the way for new approaches in the direction of using negative probabilities in macroeconomic modelling.
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