The space of outcomes of semi-static trading strategies need not be closed

Beatrice Acciaio (), Martin Larsson () and Walter Schachermayer ()
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Beatrice Acciaio: London School of Economics and Political Science
Martin Larsson: Department of Mathematics
Walter Schachermayer: Universität Wien

Finance and Stochastics, 2017, vol. 21, issue 3, No 5, 751 pages

Abstract: Abstract Semi-static trading strategies make frequent appearances in mathematical finance, where dynamic trading in a liquid asset is combined with static buy-and-hold positions in options on that asset. We show that the space of outcomes of such strategies can have very poor closure properties when all European options for a fixed date T $T$ are available for static trading. This causes problems for optimal investment, and stands in sharp contrast to the purely dynamic case classically considered in mathematical finance.

Keywords: Semi-static trading strategies; Semi-static completeness; Semi-static replication; 60H05; 60H30 (search for similar items in EconPapers)
JEL-codes: G12 G13 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s00780-017-0329-3

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