J. Comp. Math., 28 (2010), pp. 569-578.


ON EQUILIBRIUM PRICING AS CONVEX OPTIMIZATION

Lihua Chen 1, Yinyu Ye 2, Jiawei Zhang 3

1 Guanghua School of Management, Peking University, Beijing 100871, China
2 Department of Management Science and Engineering, Stanford University, Stanford, CA 94305, USA
3 IOMS-Operations Management, Stern School of Business, New York University, New York, NY 10012, USA

Received 2009-6-20 Accepted 2009-7-3
Available online 2010-5-1
doi:10.4208/jcm.1003-m0001

Abstract

We study competitive economy equilibrium computation. We show that, for the first time, the equilibrium sets of the following two markets: 1. A mixed Fisher and Arrow-Debreu market with homogeneous and log-concave utility functions; 2. The Fisher and Arrow-Debreu markets with several classes of concave non-homogeneous utility functions; are convex or log-convex. Furthermore, an equilibrium can be computed as convex optimization by an interior-point algorithm in polynomial time.

Key words: Convex optimization, Competitive economy equilibrium, Non-homogeneous utility

AMS subject classifications: 90C25, 91B50


Email: chenlh@gsm.pku.edu.cn, yinyu-ye@stanford.edu, jzhang@stern.nyu.edu
 

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