Large Financial Markets and Asymptotic Arbitrage with Small Transaction Costs
- Working Paper
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. Show more
Pages / Article No.
Organisational unit03845 - Teichmann, Josef / Teichmann, Josef
NotesSubmitted 2 November 2012.
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