Duality Theory for Portfolio Optimisation under Transaction Costs

2014/08/26 by Christoph Czichowsky, Czichowsky, Christoph, Walter Schachermayer +1 · 2 citations
Economics, Econometrics and Finance · #60G48 #91G10 #93E20 #Economic theories and models #FOS: Economics and business #Financial Markets and Investment Strategies #Mathematical Finance (q-fin.MF) #Portfolio Management (q-fin.PM) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1408.5989

openalex publication_date 2014/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For portfolio optimisation under proportional transaction costs, we provide a duality theory for general cadlag price processes. In this setting, we prove the existence of a dual optimiser as well as a shadow price process in a generalised sense. This shadow price is defined via a "sandwiched" process consisting of a predictable and an optional strong supermartingale and pertains to all strategies which remain solvent under transaction costs. We provide examples showing that in the present general setting the shadow price process has to be of this generalised form.

Cited by

• Optimal Investment with Random Endowments and Transaction Costs: Duality Theory and Shadow Prices
• Discrete time shadow price revisited

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