On statistical indistinguishability of complete and incomplete discrete time market models

We investigate the possibility of statistical evaluation of the market completeness for discrete timestock market models. It is known that the market completeness isnot a robust property: small random deviations of the coefficientsconvert a complete market model into a incomplete one. The papershows that market incompleteness is also non-robust.We show that, for any incomplete market from a wideclass of discrete time models, there exists a complete market model witharbitrarily close stock prices. This means that incomplete markets are indistinguishable from the complete markets in the terms of market statistics