The possibility of statistical evaluation of the market completeness and incompleteness is investigated for continuous time diffusion stock market models. It is  shown that, for any incomplete market model from a wide class of models, there exists a complete market model with an arbitrarily close paths of the stock prices. This leads to the counterintuitive conclusion that the incomplete markets are indistinguishable from the complete markets in the terms of the price statistics.
The possibility of statistical evaluation of the market completeness and incompleteness is investigated for continuous time diffusion stock market models. It is well known that market completeness is not a robust property: a complete market model can be made incomplete via small random deviations of the coefficients. 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 model from a wide class of models, there exists a complete market model with an arbitrarily close paths of the stock prices. This leads to the counterintuitive conclusion that the incomplete markets are indistinguishable from the complete markets in the terms of the price statistics.
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well known that market completeness is not a robust property: a complete market model can be made incomplete via small random deviations of the coefficients. 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