Before revision: Equivalent characterizations of multi-portfolio time consistency are deduced for closed convex and coherent set-valued risk measures on L^p_d  . In the convex case, multi-portfolio time consistency is equivalent to a  condition on the sum of minimal penalty functions.
After revision: Equivalent characterizations of multi-portfolio time consistency are deduced for closed convex and coherent set-valued risk measures on L^p_d . In the convex case, multi-portfolio time consistency is equivalent to a cocycle condition on the sum of minimal penalty functions.