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June 2016 Duality theory for portfolio optimisation under transaction costs
Christoph Czichowsky, Walter Schachermayer
Ann. Appl. Probab. 26(3): 1888-1941 (June 2016). DOI: 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.


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Christoph Czichowsky. Walter Schachermayer. "Duality theory for portfolio optimisation under transaction costs." Ann. Appl. Probab. 26 (3) 1888 - 1941, June 2016.


Received: 1 August 2014; Revised: 1 August 2015; Published: June 2016
First available in Project Euclid: 14 June 2016

zbMATH: 06618845
MathSciNet: MR3513609
Digital Object Identifier: 10.1214/15-AAP1136

Primary: 60G48, 91G10, 93E20

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.26 • No. 3 • June 2016
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