Incomplete-Market Equilibria Solved Recursively on an Event Tree

Abstract

We develop a method that allows one to compute incomplete-market equilibria routinely for Markovian equilibria (when they exist). The main difficulty to be overcome arises from the set of state variables. There are, of course, exogenous state variables driving the economy but, in an incomplete market, there are also endogenous state variables, which introduce path dependence. We write on an event tree the system of all first-order conditions of all times and states and solve recursively for state prices, which are dual variables. We illustrate this "dual" method and show its many practical advantages by means of several examples.

Keywords: incomplete market, financial-market equilibrium, computation, recursive methods

JEL Classification: C63, C68, D52, D58, D91, G11, G12.