Duality theory for portfolio optimisation under transaction costs

Christoph Czichowsky and Walter Schachermayer

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

Abstract: 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.

Keywords: utility maximisation; proportional transaction costs; convex duality; shadow prices; supermartingale deflators; optional strong supermartingales; predictable strong supermartingales; logarithmic utility (search for similar items in EconPapers)
JEL-codes: C61 G11 (search for similar items in EconPapers)
Date: 2016-06-14
New Economics Papers: this item is included in nep-upt
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Citations: View citations in EconPapers (23)

Published in Annals of Applied Probability, 14, June, 2016, 26(3), pp. 1888-1941. ISSN: 1050-5164

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