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

Christoph Johannes Czichowsky, Rémi Peyre, Walter Schachermayer and Junjian Yang

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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)
JEL-codes: C61 G11 (search for similar items in EconPapers)
Date: 2018-01-01
New Economics Papers: this item is included in nep-upt
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Citations: View citations in EconPapers (8)

Published in Finance and Stochastics, 1, January, 2018, 22(1), pp. 161-180. ISSN: 0949-2984

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