, Volume 7, Issue 4, pp 533-553

Arbitrage in fractional Brownian motion models

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Abstract.

We construct arbitrage strategies for a financial market that consists of a money market account and a stock whose discounted price follows a fractional Brownian motion with drift or an exponential fractional Brownian motion with drift. Then we show how arbitrage can be excluded from these models by restricting the class of trading strategies.

Manuscript received: February 2002; final version received: November 2002
This paper is part of the author's doctoral dissertation written under the supervision of Freddy Delbaen. Financial support from Credit Suisse is gratefully acknowledged.