Arbitrage in fractional Brownian motion models
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.
scientific article; zbMATH DE number 2059116