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

In an L <Superscript>∞</Superscript>-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