Big data, machine learning and AI inverts adverse selection problems. It allows insurers to infer statistical information and thereby reverses information advantage from the insuree to the insurer. In a setting with two-dimensional type space whose correlation can be inferred with big data we derive three results: First, a novel tradeoff between a belief gap and price discrimination emerges. The insurer tries to protect its statistical information by offering only a few screening contracts. Second, we show in a setting with naïve agents that do not perfectly infer statistical information from the price of offered contracts, price discrimination significantly boosts insurer’s profits. Third, introducing competition sucks out the informational advantage of the insurer, and forcing the monopolistic insurer to reveal its statistical information can be helpful to the insuree even though it may reduce total surplus. We also discuss the significance of our analysis through four stylized facts: the rise of data brokers, the perils of market concentration with advent of big data, the importance of consumer activism and regulatory forbearance, and the merits of a public data repository.