Conditional interior and conditional closure of a random set

Meriam El Mansour (1) , Emmanuel Lépinette (2)

1 Université Paris Dauphine-PSL
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

In this paper, we introduce two new concepts of conditional random set in a Banach space: The conditional interior and the conditional closure. The conditional interior is an open version of the conditional core, as recently introduced by Lépinette and Molchanov, and may be seen as a measurable version of the topological interior. The conditional closure generalizes the concept of conditional support. These concepts are useful for applications in mathematical finance and conditional optimization.

Mots clés: Random set; conditional core; conditional interior; conditional closure; random optimization; mathematical finance

Domaines: Probabilités [math.PR]

Meriam El Mansour, Emmanuel Lépinette. Conditional interior and conditional closure of a random set. Journal of Optimization Theory and Applications, 2020, 187. ⟨hal-02272243⟩