Finance and Stochastics

, Volume 17, Issue 3, pp 587–613 | Cite as

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

  • Jocelyne Bion-Nadal
  • Giulia Di Nunno


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.


Price operator Dynamic risk measure Extension theorem Representation theorem Fundamental theorem Equivalent martingale measure Good deal 

Mathematics Subject Classification (2010)

46E30 91B70 

JEL Classification

G12 G13 



This research was mainly carried through during the visit of G. Di Nunno at Ecole Polytechnique with the support of Chair of Financial Risks of the Risk Foundation, Paris, and the visit of J. Bion-Nadal at University of Oslo with the support of CMA—Centre of Mathematics for Applications.


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.UMR 7641 CNRS-Ecole PolytechniqueEcole PolytechniquePalaiseau CedexFrance
  2. 2.Centre of Mathematics for Applications (CMA), Department of MathematicsUniversity of OsloOsloNorway
  3. 3.Norwegian School of Economics and Business Administration (NHH)BergenNorway

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