ORIE Colloquium on 11/18/2014 - Patrick Cheridito: Equilibrium Pricing under Translation Invariant Preferences

Abstract: A general discrete-time framework for deriving equilibrium prices of financial assets is proposed. It allows for heterogenous agents, unspanned random endowments and convex trading constraints. A dual characterization of equilibria is given, and general results on their existence and uniqueness are provided. In the special case where all agents have preferences of the same type and in equilibrium, all random endowments are replicable by trading in the financial market, a one-fund theorem holds, and an explicit expression for the equilibrium pricing kernel can be given. If the underlying noise is generated by finitely many Bernoulli random walks, the equilibrium dynamics can be described by a system of coupled backward stochastic difference equations, which in the continuous-time limit becomes a multidimensional backward stochastic differential equation. If the market is complete in equilibrium, the system of equations decouples, but if not, one needs to keep track of the prices and continuation values of all agents to solve it.