In the past decades, risk management in the financial community has been dominated by data-intensive statistical methods which rely on short historical time series to estimate future risk. Many observers consider this approach as a contributor to the current financial crisis, as a long period of low volatility gave rise to an illusion of control from the perspectives of both regulators and the regulated. The crucial question is whether there is an alternative. There are voices which claim that there is no reliable way to detect bubbles, and that crashes can be modeled as exogenous black swans. Others claim that dragon kings, or crashes which result from endogenous dynamics, can be understood and therefore be predicted, at least in principle. The authors suggest that the concept of Bayesian risk management may efficiently mobilize the knowledge, comprehension, and experience of experts in order to understand what happens in financial markets.