Financial Market Equilibria with Cumulative Prospect Theory

The paper rst shows that nancial market equilibria need not to exist if agents possesscumulative prospect theory preferences with piecewise-power value functions. This is due tothe boundary behavior of the cumulative prospect theory value function, which might causean innite short-selling problem. But even when a nonnegativity constraint on nal wealthis added, non-existence can occur due to the non-convexity of CPT preferences, which mightcause discontinuities in the agents' demand functions. This latter observation also impliesthat concavication arguments which has been used in portfolio allocation problems with CPTpreferences do not apply to our general equilibrium setting with nite many agents. Existenceof equilibria is established when non-negativity constraints on nal wealth are imposed andthere is a continuum of agents in the market. However, if the original prospect theory isused instead of cumulative prospect theory, then other discontinuity problems can cause nonexistenceof market equilibria even in this case.