Arbitrage with fractional Brownian motion. (English) Zbl 0884.90045

Rogers, L. C. G.

Math. Finance 7, No. 1, 95-105 (1997).

Summary: Fractional Brownian motion has been suggested as a model for the movement of log share prices which would allow long-range dependence between returns on different days. While this is true, it also allows arbitrage opportunities, which we demonstrate both indirectly and by constructing such an arbitrage. Nonetheless, it is possible by looking at a process similar to the fractional Brownian motion to model long-range dependence of returns while avoiding arbitrage.

MSC:

91G80	Financial applications of other theories
60G22	Fractional processes, including fractional Brownian motion
60G35	Signal detection and filtering (aspects of stochastic processes)
91B62	Economic growth models

Keywords:

fractional Brownian motion; Brownian motion; arbitrage; long-range dependence; equivalent martingale measure