Large pension plans face the difficulty of investing premiums in a financially prudent but economically efficient way. An investment concept used in industry, e.g., by pension funds, is risk budgeting portfolios (RBP). RBP are diversified portfolios where the diversification is on the level of the risk contribution of each asset to the risk of the total portfolio loss. In this work, we assess the risk of the portfolio via a coherent risk measure, such as the Expected Shortfall. The risk contribution of an asset, is then the added risk of marginally increasing the portfolio’s position in that asset. Hence, risk budgeting portfolios are diversified in terms of the risk stemming from each asset and therefore ideal for pension plans which face stringent investment requirements. Advances in the academic literature and practical implementations of RBP strategies, however, make the strong assumption that assets are multivariate Gaussian. We propose an efficient stochastic optimization framework that calculates RBP for assets with arbitrary joint distribution. Moreover, the RBP is constructed using only sampled scenarios, making it applicable in a variety of settings such as data-driven statistical models, arbitrary dependency structures, and internal loss models.