We consider a two-stage stochastic multi-objective linear program (TSSMOLP) which is a natural multi-objective generalization of the well-studied two-stage stochastic linear program. The second-stage recourse decision is governed by an uncertain multi-objective linear program whose solution maps to an uncertain second-stage nondominated set. The TSSMOLP then comprises the objective function, which is the Minkowsi sum of a linear term plus the expected value of the second-stage nondominated set, and the constraints, which are linear. Since the second-stage nondominated set is a random set, its expected value is defined through the selection expectation. We prove properties of TSSMOLPs and the multifunctions that arise therein, including that the global Pareto set of a TSSMOLP with two or more objectives is cone-convex on a general probability space. We also prove that two reformulations of the TSSMOLP are nondominance-equivalent to the original; these reformulations facilitate mathematical analysis and the future development of TSSMOLP solution methods.
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