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- Title
Asymptotic arbitrage with small transaction costs.
- Authors
Klein, Irene; Lépinette, Emmanuel; Perez-Ostafe, Lavinia
- Abstract
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 on market n, in terms of contiguity properties of sequences of equivalent probability measures induced by λ-consistent price systems. These results are analogous to the frictionless case; compare (Kabanov and Kramkov in Finance Stoch. 2:143-172, ; Klein and Schachermayer in Theory Probab. Appl. 41:927-934, ). 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, ) 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>0 on market n; there does not exist any form of asymptotic arbitrage. In one case, ( λ) can even converge to 0, but not too fast.
- Subjects
ASYMPTOTIC expansions; ARBITRAGE; TRANSACTION costs; FINANCIAL markets; PRICING; ECONOMIC convergence
- Publication
Finance & Stochastics, 2014, Vol 18, Issue 4, p917
- ISSN
0949-2984
- Publication type
Article
- DOI
10.1007/s00780-014-0242-y