  Motivated by liquidity risk in mathematical finance, D. Lacker introduced
concentration inequalities for risk measures, i.e. upper bounds on the
\emph{liquidity risk profile} of a financial loss. We derive these inequalities
in the case of time-consistent dynamic risk measures when the filtration is
assumed to carry a Brownian motion. The theory of backward stochastic
differential equations (BSDEs) and their dual formulation plays a crucial role
in our analysis. Natural by-products of concentration of risk measures are a
description of the tail behavior of the financial loss and transport-type
inequalities in terms of the generator of the BSDE, which in the present case
can grow arbitrarily fast.
