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Arbitrage in fractional Brownian motion models. (English) Zbl 1035.60036
The author considers a financial market on a compact interval where money can be invested in 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. Different notions of arbitrage are given and trading strategies are specified. Then arbitrage strategies consisting of combinations of buy and hold strategies are constructed. At last, it is shown that arbitrage can be excluded from models by introducing a minimal amount of time that must lie between two consecutive transactions.

MSC:
60G15 Gaussian processes
60G22 Fractional processes, including fractional Brownian motion
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
91G10 Portfolio theory
91B24 Microeconomic theory (price theory and economic markets)
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