  We define and develop an approach for risk budgeting allocation - a risk
diversification portfolio strategy - where risk is measured using a dynamic
time-consistent risk measure. For this, we introduce a notion of dynamic risk
contributions that generalise the classical Euler contributions and which allow
us to obtain dynamic risk contributions in a recursive manner. We prove that,
for the class of coherent dynamic distortion risk measures, the risk allocation
problem may be recast as a sequence of strictly convex optimisation problems.
Moreover, we show that self-financing dynamic risk budgeting strategies with
initial wealth of 1 are scaled versions of the solution of the sequence of
convex optimisation problems. Furthermore, we develop an actor-critic approach,
leveraging the elicitability of dynamic risk measures, to solve for risk
budgeting strategies using deep learning.
