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.
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