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This paper lays the mathematical foundations of the notion of an investment's sustainability return and investigates three different models of portfolio selection with probabilistic constraints for safety first investors caring about the financial and the sustainability consequences of their investments. The discussion of these chance-constrained programming problems for stochastic and deterministic sustainability returns includes theoretical results especially on the existence of a unique solution under certain conditions, an illustrating example, and a computational time analysis. Furthermore, the authors conclude that a simple convex combination of financial and sustainability returns - yielding a new univariate decision variable - is not sufficiently general.
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