Risk Budgeting Allocation for Dynamic Risk Measures

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 generalize the classical Euler contributions, which allows 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 optimization problems. Moreover, we show that self-financing dynamic risk budgeting strategies with initial wealth of one are scaled versions of the solution of the sequence of convex optimization problems. Furthermore, we develop an actor-critic approach, leveraging the elicitability of dynamic risk measures, to solve for risk budgeting strategies using deep learning.