Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs

Christoph Czichowsky (), Rémi Peyre (), Walter Schachermayer and Junjian Yang
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Christoph Czichowsky: LSE - London School of Economics and Political Science
Rémi Peyre: IECL - Institut Élie Cartan de Lorraine - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique, Fakultät für Mathematik [Wien] - Universität Wien = University of Vienna
Walter Schachermayer: ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich], Fakultät für Mathematik [Wien] - Universität Wien = University of Vienna
Junjian Yang: Fakultät für Mathematik [Wien] - Universität Wien = University of Vienna, CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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Abstract: The present paper accomplishes a major step towards a reconciliation of two conflicting approaches in mathematical finance: on the one hand, the mainstream approach based on the notion of no arbitrage (Black, Merton & Scholes); and on the other hand, the consideration of non-semimartingale price processes, the archetype of which being fractional Brownian motion (Mandelbrot). Imposing (arbitrarily small) proportional transaction costs and considering logarithmic utility optimisers, we are able to show the existence of a semimartingale, frictionless shadow price process for an exponential fractional Brownian financial market.

Keywords: proportional transaction costs; fractional Brownian motion; shadow prices; two-way crossing; logarithmic utility (search for similar items in EconPapers)
Date: 2018
New Economics Papers: this item is included in nep-upt
Note: View the original document on HAL open archive server: https://hal.science/hal-02373296v1
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Citations: View citations in EconPapers (6)

Published in Finance and Stochastics, 2018, 22 (1), pp.161-180. ⟨10.1007/s00780-017-0351-5⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02373296

DOI: 10.1007/s00780-017-0351-5

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