# On statistical indistinguishability of the complete and incomplete markets

**Authors:** Nikolai Dokuchaev  
**arXiv:** [1209.4695](https://arxiv.org/abs/1209.4695)  
**Date:** 2012-09-21  
**Summary page:** https://www.summarizepaper.com/fr/paper/1209.4695v3/

## Abstract

The possibility of statistical evaluation of the market completeness and incompleteness is investigated for continuous time diffusion stock market models. It is known that the market completeness is not a robust property: small random deviations of the coefficients convert a complete market model into a incomplete one. The paper shows that market incompleteness is also non-robust: small deviations can convert an incomplete model into a complete one. More precisely, it is shown that, 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. This leads to a counterintuitive conclusion that the incomplete markets are indistinguishable from the complete markets in the terms of the market statistics.