Essential Supremum with Respect to a Random Partial Order

Emmanuel Lépinette (1) , Yuri Kabanov (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

Inspired by the theory of financial markets with transaction costs, we study a concept of essential supremum in the framework where a random partial order in $\R^d$ is lifted to the space $L^0(\R^d)$ of $d$-dimensional random variables. In contrast to the classical definition, we define the essential supremum as a subset of random variables satisfying some natural properties. An application of the introduced notion to a hedging problem under transaction costs is given.

Mots clés: Essential supremum; random partial order

Domaines: Probabilités [math.PR]

Emmanuel Lépinette, Yuri Kabanov. Essential Supremum with Respect to a Random Partial Order. 2012. ⟨hal-00608856v3⟩