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Coherent Risk Measure On L0: Na Condition, Pricing And Dual Representation

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  • EMMANUEL LEPINETTE

    (Ceremade, UMR CNRS 7534, Paris Dauphine University, PSL National Research, Place du Maréchal De Lattre De Tassigny, 75775 Paris cedex 16, France†Gosaef, Faculty of Sciences of Tunis, Tunisia)

  • DUC THINH VU

    (��Gosaef, Faculty of Sciences of Tunis, Tunisia)

Abstract

The NA condition is one of the pillars supporting the classical theory of financial mathematics. We revisit this condition for financial market models where a dynamic risk-measure defined on L0 is fixed to characterize the family of acceptable wealths that play the role of nonnegative financial positions. We provide in this setting a new version of the fundamental theorem of asset pricing and we deduce a dual characterization of the super-hedging prices (called risk-hedging prices) of a European option. Moreover, we show that the set of all risk-hedging prices is closed under NA. At last, we provide a dual representation of the risk-measure on L0 under some conditions.

Suggested Citation

  • Emmanuel Lepinette & Duc Thinh Vu, 2021. "Coherent Risk Measure On L0: Na Condition, Pricing And Dual Representation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(06n07), pages 1-26, September.
    • Handle: RePEc:wsi:ijtafx:v:24:y:2021:i:06n07:n:s0219024921500370
    DOI: 10.1142/S0219024921500370
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