Seoul Journal of Economics - Vol. 30 , No. 4

[ Article ]
Seoul Journal of Economics - Vol. 30, No. 4, pp. 471-486
Abbreviation: SJE
ISSN: 1225-0279 (Print)
Print publication date 30 Nov 2017
Received 28 Jul 2017 Revised 10 Oct 2017 Accepted 02 Nov 2017

One-Fund Separation and Uniqueness of Equilibrium in Incomplete Markets with Heterogeneous Beliefs
Dong Chul Won
Dong Chul Won, School of Business, Ajou University, 206 Worldcup-ro, Yeongtong-gu, Suwon 16499, South Korea, Tel: +82-31-219-2708 (dcwon@ajou.ac.kr)

Funding Information ▼

JEL Classification: D52, C62, G11, C02


Uniqueness of equilibrium is a relatively unexplored issue in incomplete markets compared with complete markets. This work shows that one-fund separation is sufficient for the uniqueness of equilibrium in a special class of incomplete markets with two agents and two assets. Specifically, it provides a new condition that is necessary and sufficient for equilibrium to exhibit one-fund separation in incomplete market economies, in which two agents have identical homothetic preferences, heterogeneous beliefs, and initial endowments spanned by asset payoffs. The new condition that is jointly imposed on heterogeneous beliefs and asset payoffs is distinct from time-honored conditions, such as gross substitution and restrictions on the Mitjushin–Polterovich coefficient. One-fund separation provides a new perspective into the uniqueness of equilibrium in incomplete markets.

Keywords: Uniqueness of equilibrium, One-fund separation, Incomplete markets, Heterogeneous beliefs, Homothetic preferences


This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2012-S1A5A2A-01018422). The author appreciates the useful comments and suggestions of two anonymous referees.

1. Bettzüge, M. C. “An Extension of a Theorem by Mitjushin and Polterovich to Incomplete Markets.” Journal of Mathematical Economics 30 (No. 3 1998): 285-300.
2. Detemple, J., and P. Gottardi. “Aggregation, Efficiency and Mutual Fund Separation in Incomplete Markets.” Economic Theory 11 (No. 2 1998): 443-455.
3. Geanakoplos, J. and K. Walsh. “Uniqueness and Stability of Equilibrium in Economies with Two Goods,” Cowles Foundation Discussion Paper No. 2050, 2016.
4. Hens, T. and A. Loeffler. “Gross Substitution in Financial Markets.” Economics Letters. 49 (1995): 39-43.
5. Hens, T. and B. Pilgrim. General Equilibrium Foundations of Finance. Boston: Kluwer Academic Publishers, 2002.
6. Magill, M. and M. Quinzii. Theory of Incomplete Markets. Cambridge: MIT University Press, 1996.
7. Pilgrim, B. “Non-Equivalence of Uniqueness of Equilibria in Complete and in Incomplete Market Models.” Research in Economics 56 (No. 2 2002): 143-156.