Superreplication under model uncertainty in discrete time

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• 作者：Marcel Nutz (1)
  
• 关键词：Knightian uncertainty ; Nondominated model ; Superreplication ; Martingale measure ; Medial limit ; Hahn鈥揃anach theorem ; 60G42 ; 91B25 ; 93E20 ; D81 ; G12
• 刊名：Finance and Stochastics
• 出版年：2014
• 出版时间：October 2014
• 年：2014
• 卷：18
• 期：4
• 页码：791-803
• 全文大小：549 KB
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• 作者单位：Marcel Nutz (1)
  
  1. Department of Mathematics, Columbia University, New York, NY, 10027, USA
  
• ISSN：1432-1122

文摘

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.