Dynamic no-good-deal pricing measures and extension theorems for linear operators on L ∞

Jocelyne Bion-Nadal () and Giulia Nunno ()

Finance and Stochastics, 2013, vol. 17, issue 3, 587-613

Abstract: In an L ∞ -framework, we present majorant-preserving and sandwich-preserving extension theorems for linear operators. These results are then applied to price systems derived by a reasonable restriction of the class of applicable equivalent martingale measures. Our results prove the existence of a no-good-deal pricing measure for price systems consistent with bounds on the Sharpe ratio. We treat both discrete- and continuous-time market models. Within this study we present definitions of no-good-deal pricing measures that are equivalent to the existing ones and extend them to discrete-time models. We introduce the corresponding version of dynamic no-good-deal pricing measures in the continuous-time setting. Copyright Springer-Verlag 2013

Keywords: Price operator; Dynamic risk measure; Extension theorem; Representation theorem; Fundamental theorem; Equivalent martingale measure; Good deal; 46E30; 91B70; G12; G13 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s00780-012-0195-y

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