An extension of a theorem by Mitjushin and Polterovich to incomplete markets

This paper generalises the Mitjushin–Polterovich theorem to the case of economies with incomplete financial markets where utility functions are of the von-Neumann–Morgenstern type. We thus give a sufficient condition on the joint distribution of the asset payoffs and the endowments which guarantees strict monotonicity of individual demand functions if the utility functions display small relative risk aversion.