Equilibrium With Exponential Utility And Non-negative Consumption
The authors study a multi-period Arrow-Debreu equilibrium in a heterogeneous economy populated by agents trading in a complete market. Each agent is represented by an exponential utility function, where additionally no negative level of consumption is permitted. They derive an explicit formula for the optimal consumption policies involving a put option depending on the state price density. They exploit this formula to prove the existence of equilibrium and then provide a characterization of all possible equilibria, under the assumption of positive endowments. Via particular examples, they demonstrate that uniqueness is not always guaranteed. Finally, they discover the presence of infinitely many equilibria when endowments are vanishing.