The relations among the three kinds of conditional risk measures (Q477159)

The paper studies the relations among the three kinds of conditional risk measures, so-called \(L^{\infty}({\mathcal E})\)-conditional risk measure, \(L^{p}({\mathcal E})\)-conditional risk measure (\(1\leq p<+\infty\)) and \(L^{p}_{{\mathcal F}}({\mathcal E})\)-conditional risk measure. Most of the results of this paper were announced in \textit{T. Guo}'s survey paper [Sci. China, Math. 54, No. 4, 633--660 (2011; Zbl 1238.46058)], but without detailed proofs. The present paper fills this gap out. Also, this paper is the third part of the authors' manuscript ``On random convex analysis -- the analytic foundation of the module approach to conditional risk measures'' [Preprint, \url{arXiv:1210.1848}].