  Risk budgeting is a portfolio strategy where each asset contributes a
prespecified amount to the aggregate risk of the portfolio. In this work, we
propose an efficient numerical framework that uses only simulations of returns
for estimating risk budgeting portfolios. Besides a general cutting planes
algorithm for determining the weights of risk budgeting portfolios for
arbitrary coherent distortion risk measures, we provide a specialised version
for the Expected Shortfall, and a tailored Stochastic Gradient Descent (SGD)
algorithm, also for the Expected Shortfall. We compare our algorithm to
standard convex optimisation solvers and illustrate different risk budgeting
portfolios, constructed using an especially designed Julia package, on real
financial data and compare it to classical portfolio strategies.

Portfolio Management;Risk Management