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

Czichowsky, Christoph Johannes, Peyre, Rémi, Schachermayer, Walter and Yang, Junjian (2018) Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs. Finance and Stochastics, 22 (1). ISSN 0949-2984

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Identification Number: 10.1007/s00780-017-0351-5

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

Item Type: Article
Official URL: https://link.springer.com/journal/780
Additional Information: © 2017 Springer-Verlag GmbH
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
JEL classification: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C61 - Optimization Techniques; Programming Models; Dynamic Analysis
G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice; Investment Decisions
Sets: Departments > Mathematics
Date Deposited: 10 Nov 2017 15:24
Last Modified: 20 Nov 2019 05:25
URI: http://eprints.lse.ac.uk/id/eprint/85230

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