Diversification and its links with risk measures

A new approach is proposed to the concept of diversification of investment portfolios which is defined as a binary relationship in the set of portfolios with finite first moments. It is shown that this relationship is, in some sense, a partial ordering. Important properties of such a definition are considered as well as necessary and sufficient condition of the comparability of portfolios, based on the coherent risk measure Expected Shortfall. As an example, an interpretation of the diversification of information risks is presented.