Asymptotic arbitrage with small transaction costs

We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for a sequence of financial markets with small proportional transaction costs λ n on market n , in terms of contiguity properties of sequences of equivalent probability measures induced...

Full description

Saved in:
Bibliographic Details
Published in:Finance and stochastics 2014-10, Vol.18 (4), p.917-939
Main Authors: Klein, Irene, Lépinette, Emmanuel, Perez-Ostafe, Lavinia
Format: Article
Language:English
Subjects:
Arbitrage
Asymptotic methods
Capital market
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Insurance
Management
Mathematics
Mathematics and Statistics
Pricing of Securities
Probability
Probability Theory and Stochastic Processes
Quantitative analysis
Quantitative Finance
Securities markets
Statistics for Business
Studies
Transaction costs
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for a sequence of financial markets with small proportional transaction costs λ n on market n , in terms of contiguity properties of sequences of equivalent probability measures induced by λ n -consistent price systems. These results are analogous to the frictionless case; compare (Kabanov and Kramkov in Finance Stoch. 2:143–172, 1998 ; Klein and Schachermayer in Theory Probab. Appl. 41:927–934, 1996 ). Our setting is simple, each market n contains two assets. The proofs use quantitative versions of the Halmos–Savage theorem (see Klein and Schachermayer in Ann. Probab. 24:867–881, 1996 ) and a monotone convergence result for nonnegative local martingales. Moreover, we study examples of models which admit a strong asymptotic arbitrage without transaction costs, but with transaction costs λ n >0 on market n ; there does not exist any form of asymptotic arbitrage. In one case, ( λ n ) can even converge to 0, but not too fast.
ISSN:0949-2984
1432-1122
DOI:10.1007/s00780-014-0242-y