On statistical indistinguishability of complete and incomplete discrete time market models

TL;DR

This paper demonstrates that in discrete time stock market models, incomplete markets cannot be statistically distinguished from complete markets because their stock prices can be made arbitrarily close, highlighting non-robustness of market completeness.

Contribution

It proves that incomplete markets are statistically indistinguishable from complete markets by constructing close models, challenging the robustness of market completeness.

Findings

Incomplete markets can be approximated arbitrarily closely by complete markets.

Market incompleteness is non-robust under small perturbations.

Complete and incomplete markets are statistically indistinguishable in terms of market data.

Abstract

We investigate the possibility of statistical evaluation of the market completeness for discrete time 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. We show that, for any incomplete market from a wide class of discrete time models, there exists a complete market model with arbitrarily close stock prices. This means that incomplete markets are indistinguishable from the complete markets in the terms of the market statistics.