Purpose

This paper aims to investigate possibility of statistical detection of market completeness for continuous time diffusion stock market models.

Design/methodology/approach

The paper uses theory of forecasting to find criteria of predictability of market parameters such as volatilities and the appreciation rates.

Findings

It is known that the market completeness is not a robust property: small random deviations of the coefficients convert a complete market model into an incomplete one. The paper shows that market incompleteness is also non-robust: for any incomplete market from a wide class of models, there exists a complete market model with arbitrarily close paths of the stock prices and the market parameters.

Originality/value

The paper results lead to a counterintuitive conclusion that the incomplete markets are indistinguishable in the terms of the market statistics.

中文翻译：

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关于完全和不完全市场模型的统计不可区分性

目的

本文旨在研究对连续时间扩散股票市场模型进行市场完整性统计检测的可能性。

设计/方法/方法

本文使用预测理论来找到市场参数（如波动率和升值率）的可预测性标准。

发现

众所周知，市场完整性不是稳健的属性：系数的较小随机偏差会将完整的市场模型转换为不完整的模型。本文表明市场不完全也是不稳健的：对于来自各种各样模型的任何不完全市场，都存在一个具有任意接近的股价和市场参数路径的完全市场模型。

创意/价值

本文的结果导致了一个反直觉的结论，即不完全市场在市场统计方面是无法区分的。