Predictive models are increasingly being used to optimize decision-making and minimize costs. A conventional approach is predict-then-optimize: first, a predictive model is built; then, this model is used to optimize decision-making. A drawback of this approach, however, is that it only incorporates costs in the second stage. Conversely, the predict-and-optimize approach proposes learning a predictive model by directly minimizing the cost of the downstream decision-making task. This is achieved by using a task-specific loss function incorporating the costs of different outcomes in the first stage, with the eventual aim of obtaining more cost-effective decisions in the second stage.  Fraud detection can be acknowledged as an (instance-dependent) cost-sensitive classification problem, where the costs due to misclassification vary between instances, and requiring adapted approaches for learning a classification model. In this presentation, we present some classifiers that directly minimize an (instance-dependent) cost measure when learning a classification model. The methods are evaluated on real data.