On the no-arbitrage market and continuity in the Hurst parameter

2015/09/22 by Nikolai Dokuchaev, Dokuchaev, Nikolai · 1 citation
Economics, Econometrics and Finance · Mathematics · #60G22 #91G10 #91G70 #Applied mathematics #Arbitrage #Brownian motion #Complex Systems and Time Series Analysis #Discontinuity (linguistics) #Econometrics #Economic theories and models #Economics #FOS: Economics and business #Financial economics #Fractional Brownian motion #Hurst exponent #Mathematical Finance (q-fin.MF) #Mathematical analysis #Mathematical economics #Mathematics #Riemann hypothesis #Riemann problem #Riemann sum #Statistics #Stochastic processes and financial applications #msc:60G22 #msc:91G10 #msc:91G70 #q-fin.MF

paper · pdf · doi:10.48550/arxiv.1509.06472

arXiv admin note: text overlap with arXiv:1509.06112

openalex publication_date 2015/09/22 · arxiv created 2015/10/13 · arxiv updated 2015/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider a market with fractional Brownian motion with stochastic integrals generated by the Riemann sums. We found that this market is arbitrage free if admissible strategies that are using observations with an arbitrarily small delay. Moreover, we found that this approach eliminates the discontinuity of the stochastic integrals with respect to the Hurst parameter H at H=1/2.

Citations

• A smooth component of the fractional Brownian motion and optimal portfolio selection

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• On the fractional stochastic integration for random non-smooth integrands

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