Financial mathematics is generally based on probabilistic models and statistical methods. Stochastic processes are used to model random fluctuations of asset prices and to capture the relations between economic factors. Stochastic calculus and optimal control are important in the selection of investment strategies, the pricing and hedging of derivative instruments, and more generally in the theory of capital markets. Extreme value theory and stochastic simulation are fundamental in financial and actuarial risk management. Techniques from statistical machine learning are becoming increasingly important for decision making and modelling of the complex data arising in financial markets.