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Duality theory for portfolio optimisation under transaction costs

Czichowsky, Christoph and Schachermayer, Walter (2016) Duality theory for portfolio optimisation under transaction costs. Annals of Applied Probability, 26 (3). pp. 1888-1941. ISSN 1050-5164

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Identification Number: 10.1214/15-AAP1136


We consider the problem of portfolio optimisation with general càdlàg price processes in the presence of proportional transaction costs. In this context, we develop a general duality theory. In particular, we prove the existence of a dual optimiser as well as a shadow price process in an appropriate generalised sense. This shadow price is defined by means of a "sandwiched" process consisting of a predictable and an optional strong supermartingale, and pertains to all strategies that remain solvent under transaction costs. We provide examples showing that, in the general setting we study, the shadow price processes have to be of such a generalised form.

Item Type: Article
Official URL:
Additional Information: © 2016 Institute of Mathematical Statistics
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
Date Deposited: 01 Sep 2015 10:47
Last Modified: 16 May 2024 02:12
Projects: PBEZP2 137313, FA506041
Funders: Swiss National Science Foundation, European Research Council

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