Fraud is defined as the utilization of deception for illegal gain by hiding the true nature of the activity. While organizations lose around $3.7 trillion in revenue due to financial crimes and fraud worldwide, they can affect all levels of society significantly. In this dissertation, I focus on credit card fraud in online transactions. Every online transaction comes with a fraud risk and it is the merchant's liability to detect and stop fraudulent transactions. Merchants utilize various mechanisms to prevent and manage fraud such as automated fraud detection systems and manual transaction reviews by expert fraud analysts. Many proposed solutions mostly focus on fraud detection accuracy and ignore financial considerations. Also, the highly effective manual review process is overlooked. First, I propose Profit Optimizing Neural Risk Manager (PONRM), a selective classifier that (a) constitutes optimal collaboration between machine learning models and human expertise under industrial constraints, (b) is cost and profit sensitive. I suggest directions on how to characterize fraudulent behavior and assess the risk of a transaction. I show that my framework outperforms cost-sensitive and cost-insensitive baselines on three real-world merchant datasets. While PONRM is able to work with many supervised learners and obtain convincing results, utilizing probability outputs directly from the trained model itself can pose problems, especially in deep learning as softmax output is not a true uncertainty measure. This phenomenon, and the wide and rapid adoption of deep learning by practitioners brought unintended consequences in many situations such as in the infamous case of Google Photos' racist image recognition algorithm; thus, necessitated the utilization of the quantified uncertainty for each prediction. There have been recent efforts towards quantifying uncertainty in conventional deep learning methods (e.g., dropout as Bayesian approximation); however, their optimal use in decision making is often overlooked and understudied. Thus, I present a mixed-integer programming framework for selective classification called MIPSC, that investigates and combines model uncertainty and predictive mean to identify optimal classification and rejection regions. I also extend this framework to cost-sensitive settings (MIPCSC) and focus on the critical real-world problem, online fraud management and show that my approach outperforms industry standard methods significantly for online fraud management in real-world settings.