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arXiv · 2405.06764

Coherent Risk Measure on $L^0$: NA Condition, Pricing and Dual Representation

Emmanuel Lepinette·Duc Thinh Vu
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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 $L^0$ is fixed to characterize the family of acceptable wealths that play the role of non negative 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 $L^0$ under some conditions.

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Emmanuel Lepinette, Duc Thinh Vu. 2024-05-10. Coherent Risk Measure on $L^0$: NA Condition, Pricing and Dual Representation. https://doi.org/10.1142/s0219024921500370

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