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Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences

Patrick Cheridito

Princeton University

Ulrich Horst

Humboldt University of Berlin

Michael Kupper

Humboldt University of Berlin - Department of Mathematics

Traian A. Pirvu

McMaster University; University of British Columbia (UBC)

July 18, 2012

We propose a general discrete-time framework for deriving equilibrium prices of financial securities. It allows for heterogeneous agents, unspanned random endowments and convex trading constraints. We give a dual characterization of equilibria and provide general results on their existence and uniqueness. 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 fi nancial market, we show that a one-fund theorem holds and give an explicit expression for the equilibrium pricing kernel. If the underlying noise is generated by nitely many Bernoulli random walks, the equilibrium dynamics can be described by a system of coupled backward stochastic di fference equations, which in the continuous-time limit becomes a multidimensional backward stochastic di fferential 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.

Number of Pages in PDF File: 30

Keywords: Competitive equilibrium, incomplete markets, heterogenous agents, trading constraints, one-fund theorem

JEL Classification: D52, D53, G12

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Date posted: February 7, 2011 ; Last revised: March 14, 2013

Suggested Citation

Cheridito, Patrick and Horst, Ulrich and Kupper, Michael and Pirvu, Traian A., Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences (July 18, 2012). Available at SSRN: http://ssrn.com/abstract=1755610 or http://dx.doi.org/10.2139/ssrn.1755610

Contact Information

Patrick Cheridito (Contact Author)
Princeton University ( email )
Princeton University
Princeton, NJ 08544
United States

Ulrich Horst
Humboldt University of Berlin ( email )
Spandauer Str. 1
Berlin, Berlin 10785
Michael Kupper
Humboldt University of Berlin - Department of Mathematics ( email )
Unter den Linden
Berlin, D-10099
Traian Adrian Pirvu
McMaster University ( email )
1280 Main Street West
Hamilton, Ontario L8S 4M4
University of British Columbia (UBC) ( email )
2329 West Mall
Vancouver, British Columbia BC V6T 1Z4
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