Bernoulli selection processes and power contractions constitute two classes of probabilistic concepts of theoretical and practical importance. The paper’s theoretical contribution consists of the development of a characterization of power contractions through the use of Bernoulli selection processes. Moreover, the interpretations in risk management, stochastic discounting modelling, and investment evaluation of Bernoulli selection processes for power contractions constitute the practical contribution. In consequence, the presence of proactivity in these disciplines makes quite clear that the results of the paper facilitate the implementations of strategic thinking, decision making, and management operations.