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

Beatrice Acciaio, Martin Larsson and Walter Schachermayer

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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 $T$ 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.

Date: 2016-06
New Economics Papers: this item is included in nep-mst and nep-net
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