On the diversity of equity markets

This is a study of the diversity of the distribution of capital in an equity market composed of stocks represented by continuous semimartingales. It is shown that for such a market, diversity is not a natural state and some mechanism such as dividend payments is needed to maintain it. Entropy is introduced as a measure of diversity and is used to study the compatibility of market diversity with capital market equilibrium. It is shown that dividend payments must be available to recycle capital from larger companies to smaller companies in order to maintain market diversity under conditions of capital market equilibrium.