A bang-bang principle for the conditional expectation vector measure

Youcef Askoura (1) , Mohammed Sbihi (2)

1 LEMMA - Laboratoire d'économie mathématique et de microéconomie appliquée
2 OPTIM - ENAC - Equipe Optim

We prove a conditional expectation bang-bang principle. Based on properties of the conditional expectation vector measure, we establish that the conditional expectation of a set-valued mapping coincides with the conditional expectation of the set of selections of its extreme points part. As a by-product, we obtain straightforwardly a purification principle.

Mots clés: onditional expectation; Lyapunov convexity theorem; Young measures; Bang- bang principle; purification principle

Domaines: Mathématiques [math]

Youcef Askoura, Mohammed Sbihi. A bang-bang principle for the conditional expectation vector measure. 2022. ⟨hal-03945255⟩