Essential Supremum in a d-dimensional Real Space with Respect to a Random Cone and Applications
Résumé
The goal of this paper is to introduce the notion of essential supremum of a family of multi-dimensional random variables with respect to a random convex cone. We give two applications in mathematical finance; We determine the ''minimal'' portfolio process super-hedging an American claim in the Kabanov dicrete-time model with transaction costs. For the same model, we construct a dynamic risk measure in a continuous-time setting. At last, we solve a Skorokhod problem with oblique reflection.
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