Incomplete-Market Equilibria Solved Recursively on an Event Tree




    Search for more papers by this author
    • Bernard Dumas is with INSEAD and with NBER and CEPR. Andrew Lyasoff is with the School of Management, Boston University. We are grateful to colleagues and students for providing valuable comments: Matthijs Breugem, Julien Cujean, Darrell Duffie, Rui Guo, Julien Hugonnier, Jens Jackwerth, Bjarne Astrup Jensen, Kenneth Judd, Felix Kubler, Abraham Lioui, Hanno Lustig, Karl Schmedders, Rafal Wojakowski, and especially 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); ESSEC, the Stockholm School of Economics, the Zurich Center for Computational Financial Economics, the Free University of Brussels (ECARES), the Wharton School, Carnegie-Mellon University, Goethe Universität (Frankfurt), INSEAD, EM Lyon; the Banque de France, the National Bank of Serbia, the Symposium on Stochastic Dynamic Models in Finance and Economics at the University of Southern Denmark, the Federal Reserve Bank of Boston, the 6th World Congress of the Bachelier Finance Society (Toronto), and the 2nd International Symposium in Computational Economics and Finance (Tunis). Dumas's research has been supported by the Swiss National Center for Competence in Research “FinRisk” and by grant 1112 of the INSEAD research fund.


Because of non-traded human capital, real-world financial markets are massively incomplete, while the modeling of imperfect, dynamic financial markets remains a wide-open and difficult field. Some 30 years after Cox, Ross, and Rubinstein (1979) taught us how to calculate the prices of derivative securities on an event tree by simple backward induction, we show how a similar formulation can be used in computing heterogeneous-agents incomplete-market equilibrium prices of primitive securities. Extant methods work forward and backward, requiring a guess of the way investors forecast the future. In our method, the future is part of the current solution of each backward time step.