In this paper, we propose three novel profit-driven strategies for churn prediction. Our proposals extend the ideas of the Minimax Probability Machine, a robust optimization approach for binary classification that maximizes sensitivity and specificity using a probabilistic setting. We adapt this method and other variants to maximize the profit of a retention campaign in the objective function, unlike most profit-based strategies that use profit metrics to choose between classifiers, and/or to define the optimal classification threshold given a probabilistic output. A first approach is developed as a learning machine that does not include a regularization term, and subsequently extended by including the LASSO and Tikhonov regularizers. Experiments on well-known churn prediction datasets show that our proposal leads to the largest profit in comparison with other binary classification techniques.