# 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/en/paper/1209.4695v3/

## Key points

- Nikolai Dokuchaev's paper investigates statistical evaluation of market completeness and incompleteness in continuous time diffusion stock market models.
- Market completeness and incompleteness are non-robust properties, meaning small random deviations of the coefficients can convert a complete model into an incomplete one or vice versa.
- 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.
- Incomplete markets are indistinguishable from complete markets in terms of their statistical properties.
- These findings have significant implications for investors and financial analysts who rely on statistical analysis to make informed decisions about investment opportunities.
- Investors should be aware that small changes in economic conditions can drastically alter their assessment of an investment opportunity's risk profile.

## Summary

In the paper "On statistical indistinguishability of the complete and incomplete markets," Nikolai Dokuchaev investigates the possibility of statistically evaluating market completeness and incompleteness in continuous time diffusion stock market models. The study reveals that both market completeness and incompleteness are non-robust properties; small random deviations of the coefficients can convert a complete model into an incomplete one, or vice versa. Specifically, Dokuchaev shows 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 incomplete markets are indistinguishable from complete markets in terms of their statistical properties. The findings have significant implications for investors and financial analysts who rely on statistical analysis to make informed decisions about investment opportunities. These results suggest that investors should be aware that small changes in economic conditions can drastically alter their assessment of an investment opportunity's risk profile.