  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.
