Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs - Archive ouverte HAL Access content directly
Journal Articles Finance and Stochastics Year : 2018

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

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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.
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Dates and versions

hal-02373296 , version 1 (20-11-2019)

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Christoph Czichowsky, Rémi Peyre, Walter Schachermayer, Junjian Yang. Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs. Finance and Stochastics, 2018, 22 (1), pp.161-180. ⟨10.1007/s00780-017-0351-5⟩. ⟨hal-02373296⟩
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