Essential Supremum with Respect to a Random Partial Order

Yuri Kabanov (1) , Emmanuel Lépinette (2)

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

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]

Yuri Kabanov, Emmanuel Lépinette. Essential Supremum with Respect to a Random Partial Order. Journal of Mathematical Economics, 2013, 49 (6), pp.478-487. ⟨10.1016/j.jmateco.2013.07.002⟩. ⟨hal-00608856v4⟩