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NO ARBITRAGE UNDER TRANSACTION COSTS, WITH FRACTIONAL BROWNIAN MOTION AND BEYOND
Author(s) -
Guasoni Paolo
Publication year - 2006
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2006.00283.x
Subject(s) - arbitrage , geometric brownian motion , transaction cost , brownian motion , mathematics , markov process , fractional brownian motion , asset (computer security) , risk arbitrage , economics , econometrics , mathematical economics , mathematical optimization , diffusion process , computer science , financial economics , finance , arbitrage pricing theory , statistics , capital asset pricing model , economy , computer security , service (business)
We establish a simple no‐arbitrage criterion that reduces the absence of arbitrage opportunities under proportional transaction costs to the condition that the asset price process may move arbitrarily little over arbitrarily large time intervals. We show that this criterion is satisfied when the return process is either a strong Markov process with regular points, or a continuous process with full support on the space of continuous functions. In particular, we prove that proportional transaction costs of any positive size eliminate arbitrage opportunities from geometric fractional Brownian motion for H ∈ (0, 1) and with an arbitrary continuous deterministic drift.