COHERENT RISK MEASURE ON L0: NA CONDITION, PRICING AND DUAL REPRESENTATION

Emmanuel Lepinette and Duc Thinh Vu ()
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2021, vol. 24, issue 06n07, 1-26

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.

Keywords: NA condition; risk-hedging prices; dynamic risk-measures; dual representation; no-arbitrage (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0219024921500370

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