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Martingale Restrictions on Equilibrium Prices of Arrow-Debreu Securities Under Rational Expectations and Consistent Beliefs

Bossaerts, Peter (1996) Martingale Restrictions on Equilibrium Prices of Arrow-Debreu Securities Under Rational Expectations and Consistent Beliefs. Social Science Working Paper, 958. California Institute of Technology , Pasadena, CA. (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20170816-162131145

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Abstract

Consider the Rational Expectations price history of an Arrow-Debreu security that matures in the money: p1; p2; …; pr. Past information can be used to predict the return pt+1 - pt) = pt. Now consider a simple alternative performance measure: (pt+1 - pt)=pt+1. It differs from the return only in that the future price is used as basis. This variable cannot be forecasted from past information. The result obtains even if investors' beliefs are biased, i.e., prices are not set in a Rational Expectations Equilibrium (REE). It depends only on investors' using the rules of conditional probability to process information. More precisely, the result continues to hold in the Bayesian Equilibrium with Consistent Beliefs (CBE) introduced by Harsanyi [1967]. Many related results are proved in this paper and extensions to the pricing of equity subject to bankruptcy risk are discussed.


Item Type:Report or Paper (Working Paper)
ORCID:
AuthorORCID
Bossaerts, Peter0000-0003-2308-2603
Additional Information:This is part of a paper that the author presented at the Université des Sciences Sociales, Toulouse, in April 1995. He is grateful for the many comments from the seminar participants. He also thanks Christian Gouriéroux for suggesting the analysis in reverse time. In addition, the paper benefited through discussions at seminars at Carnegie Mellon University, U.C. Riverside, University of Minnesota, and through comments from Oleg Bondarenko, Alan Kraus, P.C.B. Phillips and Richard Roll. Oleg Bondarenko provided able research assistance. The usual disclaimer applies.
Group:Social Science Working Papers
Subject Keywords:Arrow-Debreu Securities, Rational Expectations Equilibrium, Bayesian Equilibrium, Consistent Beliefs, Market Efficiency, Learning, Martingales, Reverse Time, Survivorship Bias.
Series Name:Social Science Working Paper
Issue or Number:958
Classification Code:JEL: C22, D84, G14
Record Number:CaltechAUTHORS:20170816-162131145
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170816-162131145
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80528
Collection:CaltechAUTHORS
Deposited By: Jacquelyn Bussone
Deposited On:17 Aug 2017 16:28
Last Modified:03 Oct 2019 18:32

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