  By adopting a distributional viewpoint on law-invariant convex risk measures,
we construct dynamics risk measures (DRMs) at the distributional level. We then
apply these DRMs to investigate Markov decision processes, incorporating latent
costs, random actions, and weakly continuous transition kernels. Furthermore,
the proposed DRMs allow risk aversion to change dynamically. Under mild
assumptions, we derive a dynamic programming principle and show the existence
of an optimal policy in both finite and infinite time horizons. Moreover, we
provide a sufficient condition for the optimality of deterministic actions. For
illustration, we conclude the paper with examples from optimal liquidation with
limit order books and autonomous driving.
