Duality theory for robust utility maximisation

Daniel Bartl, Michael Kupper, Ariel Neufeld (Korresp. Autor*in)

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

Abstract

In this paper, we present a duality theory for the robust utility maximisation problem in continuous time for utility functions defined on the positive real line. Our results are inspired by – and can be seen as the robust analogues of – the seminal work of Kramkov and Schachermayer (Ann. Appl. Probab. 9:904–950, 1999). Namely, we show that if the set of attainable trading outcomes and the set of pricing measures satisfy a bipolar relation, then the utility maximisation problem is in duality with a conjugate problem. We further discuss the existence of optimal trading strategies. In particular, our general results include the case of logarithmic and power utility, and they apply to drift and volatility uncertainty.
OriginalspracheEnglisch
Seiten (von - bis)469-503
Seitenumfang35
FachzeitschriftFinance and Stochastics
Jahrgang25
DOIs
PublikationsstatusVeröffentlicht - 2021

ÖFOS 2012

  • 101024 Wahrscheinlichkeitstheorie
  • 101007 Finanzmathematik

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