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Optimization under uncertainty has attracted recently an increasing interest in the process systems engineering literature. The inclusion of uncertainties in an optimization problem inevitably leads to the need to manage the associated risk in order to control the variability of the objective function in the uncertain parameters space. So far, risk management methods have focused on optimizing a single risk metric along with the expected performance. In this work we propose an alternative approach that can handle several risk metrics simultaneously. First, a multi-objective stochastic model containing a set of risk metrics is formulated. This model is then solved efficiently using a tailored decomposition strategy inspired on the Sample Average Approximation. After a normalization step, the resulting solutions are assessed using Pareto filters, which identify solutions showing better performance in the uncertain parameters space. The capabilities and benefits of our approach are illustrated through a design and planning supply chain case study.