Arbitrage with Fractional Brownian Motion
TL;DR: In this paper, a process similar to the fractional Brownian motion has been used to model long-range dependence of returns while avoiding arbitrage, which is shown both indirectly and by constructing such an arbitrage.
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Abstract: 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.
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References
•Book
Stochastic differential equations and diffusion processes
G. B. Kallianpur
- 01 Jan 1981
TL;DR: In this article, Stochastic Differential Equations and Diffusion Processes are used to model the diffusion process in stochastic differential equations. But they do not consider the nonlinearity of diffusion processes.
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On the fundamental theorem of asset pricing with an infinite state space
Kerry Back,Stanley R. Pliska +1 more
TL;DR: In this article, the authors consider a securities market where there is no arbitrage and a risk-neutral agent has an optimal demand subject to a minimum wealth constraint, yet there are no risk neutral probability measures and no state price density.
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