Large Financial Markets and Asymptotic Arbitrage with Small Transaction Costs
We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for large financial markets with small proportional transaction costs $\la_n$ on market $n$ in terms of contiguity properties of sequences of equivalent probability measures induced by $\la_n$--consistent price systems. These results are analogous to the frictionless case. Our setting is simple, each market $n$ contains two assets with continuous price processes. The proofs use quantitative versions of the Halmos--Savage Theorem and a monotone convergence result of nonnegative local martingales. Moreover, we present an example admitting a strong asymptotic arbitrage without transaction costs; but with transaction costs $\la_n>0$ on market $n$ ($\la_n\to0$ not too fast) there does not exist any form of asymptotic arbitrage.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ross, Stephen A., 1976.
"The arbitrage theory of capital asset pricing,"
Journal of Economic Theory,
Elsevier, vol. 13(3), pages 341-360, December.
- Stephen A. Ross, "undated". "The Arbitrage Theory of Capital Asset Pricing," Rodney L. White Center for Financial Research Working Papers 02-73, Wharton School Rodney L. White Center for Financial Research.
- Stephen A. Ross, "undated". "The Arbitrage Theory of Capital Asset Pricing," Rodney L. White Center for Financial Research Working Papers 2-73, Wharton School Rodney L. White Center for Financial Research.
- Y.M. Kabanov & D.O. Kramkov, 1998. "Asymptotic arbitrage in large financial markets," Finance and Stochastics, Springer, vol. 2(2), pages 143-172.
- Paolo Guasoni & Miklós Rásonyi & Walter Schachermayer, 2010. "The fundamental theorem of asset pricing for continuous processes under small transaction costs," Annals of Finance, Springer, vol. 6(2), pages 157-191, March.
- J. Kallsen & J. Muhle-Karbe, 2010. "On using shadow prices in portfolio optimization with transaction costs," Papers 1010.4989, arXiv.org.
- Yuri M. Kabanov & Günter Last, 2002. "Hedging under Transaction Costs in Currency Markets: a Continuous-Time Model," Mathematical Finance, Wiley Blackwell, vol. 12(1), pages 63-70.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1211.0443. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If references are entirely missing, you can add them using this form.