Handbook

Finance is concerned with making definite numerical recommendations that frequently can only be obtained by analysing sophisticated models using high-speed computers. This course studies the design, implementation and use of computer programs to solve practical mathematical problems of relevance to finance, insurance and risk management. It includes a review of MATLAB/Python, floating point numbers, rounding error and computational complexity, and a selection of topics from: approximation and parameter estimation, Fourier series and the FFT, finite difference approximations, partial differential equations (Black-Scholes PDE), sparse linear systems, nonlinear algebraic equations, trees, Monte Carlo methods and simulation, random numbers and variance reduction, numerical integration. The teaching activities include weekly lectures in which the theoretical background is explained and weekly practical computing laboratory classes.