Essential Supremum in a d-dimensional Real Space with Respect to a Random Cone and Applications

Emmanuel Denis (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Mots clés: Essential supremum; random cones; transaction costs; risk-measure; Skorokhod problem

Domaines: Probabilités [math.PR]

Emmanuel Denis. Essential Supremum in a d-dimensional Real Space with Respect to a Random Cone and Applications. 2011. ⟨hal-00608856v1⟩