Finance and Stochastics

, Volume 18, Issue 4, pp 791–803 | Cite as

Superreplication under model uncertainty in discrete time

Article

Abstract

We study the superreplication of contingent claims under model uncertainty in discrete time. We show that optimal superreplicating strategies exist in a general measure-theoretic setting; moreover, we characterize the minimal superreplication price as the supremum over all continuous linear pricing functionals on a suitable Banach space. The main ingredient is a closedness result for the set of claims which can be superreplicated from zero capital; its proof relies on medial limits.

Keywords

Knightian uncertainty Nondominated model Superreplication Martingale measure Medial limit Hahn–Banach theorem 

Mathematics Subject Classification

60G42 91B25 93E20 

JEL Classification

D81 G12 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of MathematicsColumbia UniversityNew YorkUSA

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