Roy (Safety First and the Holding of Assets, 1952) argues that decisions under uncertainty motivate firms to avoid bankruptcy. In this paper the authors ask about the behaviour of a monopolist who pre-commits to price when she has only probabilistic knowledge about demand. They argue that pricing in order to maximise the likelihood of survival explains anomalies such as inelastic pricing, why the firm takes on more risk as gains become less likely, and asymmetric responses to demand and cost changes. When demand is a linear demand, the monopolist’s response to an increase in the marginal cost is similar to the response when mark-up pricing is used. That is, there is a one-to-one relationship between an increase of the marginal cost and an increase in price.