Incomplete-Market Equilibria Solved Recursively on an Event Tree
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.
We are grateful to colleagues and students for providing valuable comments: Julien Cujean, Darrell Duffie, Julien Hugonnier, Bjarne Astrup Jensen, Felix Kubler, Pascal Maenhout, Raman Uppal and Tan Wang, as well as participants in workshops at Handelshøyskolen BI (Oslo), the Copenhagen School of Economics, the Collegio Carlo Alberto (Torino), the University of Southern Denmark, ESSEC and the Free University of Brussels (ECARES). Dumas' research is supported by the Swiss National Center for Competence in Research "FinRisk". The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research.
Incomplete-Market Equilibria Solved Recursively on an Event Tree BERNARD DUMAS, ANDREW LYASOFF† Article first published online: 12 SEP 2012 DOI: 10.1111/j.1540-6261.2012.01775.x © 2012 The American Finance Association Issue The Journal of Finance The Journal of Finance Volume 67, Issue 5, pages 1897–1941, October 2012