<Para ID="Par1">Equivalent characterizations of multi-portfolio time consistency are deduced for closed convex and coherent set-valued risk measures on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$L^{p}({\varOmega,\mathcal{F},\mathbb{P}; \mathbb{R}^{d}})$</EquationSource> </InlineEquation> with image space in the power set of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$L^{p}({\varOmega,\mathcal{F}_{t},\mathbb{P};...</equationsource></inlineequation></equationsource></inlineequation></para>

This paper aims at resolving a major obstacle to practical usage of time-consistent risk-averse decision models. The recursive objective function, generally used to ensure time consistency, is complex and has no clear/direct interpretation. Practitioners rather choose a simpler and more...