For several decades, the no-arbitrage (NA) condition and the martingale measures have played a major role in the financial asset's pricing theory. We propose a new approach for estimating the superreplication cost based on convex duality instead of martingale measures duality : Our prices will be expressed using Fenchel conjugate and biconjugate. The super-hedging problem leads endogenously to a weak condition of NA called Absence of Immediate Profit (AIP). We propose several characterizations of AIP and study the relation with the classical notions of no-arbitrage. We also give some promising numerical illustrations.

International audienceAeromagnetic and gravity data have proven to be among the most effective methods for mapping deeply buried basin/basement interfaces. However, the data interpretation generally suffers from ambiguities, due to the non-uniqueness of the gravity and magnetic signatures. Here, we tie the gravity and magnetic signatures with a petrophysical characterization of the lithologies outcropping around the French Paris Basin. Our methodology investigates the lithology and structure of its hidden Variscan substratum at the junction between the Armorican Massif and Massif Central. Our approach is based on the combination of potential field data, magnetic susceptibilities measured in the field, density values of sample rocks and information documented in boreholes, in order to propose a new interpretative geological map of the buried substratum of the Paris Basin. The petrophysical description is combined with geophysical patterns of the substratum, mapped through statistical unsupervised classification of suitably selected magnetic and gravity maps. The first step of interpretation consists in extending the outcropping major structures below the Meso-Cenozoic sedimentary cover of the Paris Basin. The litho-structural units, in between these major structures, are then interpreted separately. The second step consists in assigning lithologies within each unit, with respect to its magnetization and density (as derived from the petrophysical compilation), and mapping its extension under cover, integrating punctual borehole information. Overall, with a special emphasis on relating geophysical signatures and petrophysical characteristics of litho-structural units, this methodology permits a precise structural and lithological cartography of a segment of the buried Variscan substratum. In the southwestern part of the Paris Basin, this approach reveals: i) the limited eastward extension of Central Brittany, ii) the eastward extension of the major Cholet fault, iii) the emphasis on N150E-N160E striking fault and their N30E conjugates, controlling the opening of Permo-Carboniferous basins, and iv) the eastward extension of the Eo-Variscan suture