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: London School of Economics and Political Science, Columbia House
Rémi Peyre: Universität Wien
Walter Schachermayer: Universität Wien
Junjian Yang: École Polytechnique

Finance and Stochastics, 2018, vol. 22, issue 1, No 6, 180 pages

Abstract: 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; 91G10; 93E20; 60G48 (search for similar items in EconPapers)
JEL-codes: C61 G11 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s00780-017-0351-5

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