This article is cited in 66 papers

Short Communications

Large financial markets: asymptotic arbitrage and contiguity

Yu. M. Kabanov^a, D. O. Kramkov<sup>b

a</sup> Central Economics and Mathematics Institute, RAS
^b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We introduce a large financial market as a sequence of ordinary security market models (in continuous or discrete time). An important property of such markets is the absence of asymptotic arbitrage, i.e., a possibility to obtain “essential” nonrisk profits from “infinitesimally” small endowments. It is shown that this property is closely related to the contiguity of the equivalent martingale measures. To check the “no asymptotic arbitrage” property one can use the criteria of contiguity based on the Hellinger processes. We give an example of a large market with correlated asset prices where the absence of asymptotic arbitrage forces the returns from the assets to approach the security market line of the CAPM.

Keywords: large security market, no-arbitrage, equivalent martingale measure, contiguity of measures, Hellinger process, Capital Asset Pricing Model (CAPM).

Received: 05.07.1993

 English version: Theory of Probability and its Applications, 1994, 39:1, 182–187

Bibliographic databases:

• 
• 
•