2026-09-20T21:58:11Zhttps://ecommons.cornell.edu/server/oai/requestoai:ecommons.cornell.edu:1813/311052026-05-14T13:48:44Zcom_1813_35col_1813_47
Larsson, Martin
Resnick, Sidney Ira
Jarrow, Robert A.
Lewis, Adrian S.
2013-01-31T19:44:18Z
2017-12-20T07:00:33Z
2012-08-20
https://hdl.handle.net/1813/31105
7959848
In 1970, Fama defined an efficient market as one where prices always 'fully reflect' available information, but so far a rigorous definition has been lacking. This thesis addresses this issue by providing a definition based on economic equilibria. Efficiency is then characterized in terms of Merton's No Dominance condition together with absence of arbitrage in the sense of No Free Lunch With Vanishing Risk, as well as the existence of an equivalent (true) martingale measure for the discounted price process. The stability of the efficiency property with respect to changes in the information set is investigated. In particular, efficiency is preserved under information reduction, but not necessarily under information expansion. Next, checkable necessary and sufficient conditions for efficiency are provided for a large class of high dimensional stochastic volatility models. Finally, information reduction is studied in the inefficient setting. This leads to new results on filtration shrinkage for strict local martingales.
en_US
Essays On The Mathematics Of Market Efficiency
dissertation or thesis
application/pdf
Operations Research
Cornell University
Doctor of Philosophy
Ph. D., Operations Research
Publication
Cornell Theses and Dissertations
Larsson, Martin
5893a6ea-7af3-41d7-abc6-04bcd26ab5df
open.access
open.access
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<Abstract>In 1970, Fama defined an efficient market as one where prices always 'fully reflect' available information, but so far a rigorous definition has been lacking. This thesis addresses this issue by providing a definition based on economic equilibria. Efficiency is then characterized in terms of Merton's No Dominance condition together with absence of arbitrage in the sense of No Free Lunch With Vanishing Risk, as well as the existence of an equivalent (true) martingale measure for the discounted price process. The stability of the efficiency property with respect to changes in the information set is investigated. In particular, efficiency is preserved under information reduction, but not necessarily under information expansion. Next, checkable necessary and sufficient conditions for efficiency are provided for a large class of high dimensional stochastic volatility models. Finally, information reduction is studied in the inefficient setting. This leads to new results on filtration shrinkage for strict local martingales.</Abstract>
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