One-Fund Separation and Uniqueness of Equilibrium in Incomplete Markets with Heterogeneous Beliefs

Uniqueness of equilibrium is a relatively unexplored issue in incomplete markets compared with complete markets. This work shows that one-fund separation is sufficient for the uniqueness of equilibrium in a special class of incomplete markets with two agents and two assets. Specifically, it provides a new condition that is necessary and sufficient for equilibrium to exhibit one-fund separation in incomplete market economies, in which two agents have identical homothetic preferences, heterogeneous beliefs, and initial endowments spanned by asset payoffs. The new condition that is jointly imposed on heterogeneous beliefs and asset payoffs is distinct from time-honored conditions, such as gross substitution and restrictions on the Mitjushin–Polterovich coefficient. One-fund separation provides a new perspective into the uniqueness of equilibrium in incomplete markets.