This paper presents a new formulation for the risk averse stochastic reservoir management problem. Using recent advances in robust optimization and stochastic programming, we propose a dynamic, multi-objective model based on minimization of a multidimensional risk measure associated with floods and droughts for a hydro-electrical complex. We present our model and then identify approximate solutions using standard affine decision rules commonly found in the literature as well as lifted decision rules. Finally, we conduct thorough numerical experiments based on a real river system in Western Québec and conclude on the relative performance of families of decision rules.