On arbitrage opportunities on some types of financial market defined by fractional Brownian motion

The problem of the presence and absence of arbitrage conditions on the three types of (B,S)- market is considered in this paper. In the first case when (B,S)- market is defined by the fractional stock, the absence of martingale measure is proved. For two others models of - market which is defined by modified fractional stock in the second case and by "homogeneous" kernel in the third case, the absence of arbitrage is proved.

Keywords: fractional Brownian motion, arbitrage opportunity, investment portfolio.