Risk budgeting portfolios from simulations
提出一种仅利用收益模拟数据来估计风险预算投资组合的高效数值框架，包括通用算法和针对预期亏损的专用算法，并在真实金融数据上与传统策略对比。
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.