No simple arbitrage for fractional Brownian motion

arXiv1508.00553MaRDI QIDQ6264173

Rémi Peyre

Publication date: 3 August 2015

Abstract: We prove the following result: For $(Z_t{)}_{tinmathbfR}$ a fractional Brownian motion with arbitrary Hurst parameter, there does not exist any stopping time $au$ adapted to the natural filtration of the increments of $Z$ such that, with positive probability, $au$ a local minimum at right of the trajectory of $Z$.

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Stopping times; optimal stopping problems; gambling theory (60G40) Financial applications of other theories (91G80)

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