A rigorous account of classical portfolio theory and a simple introduction to modern risk measures and their limitations.

Maciej J. Capi¿ski is an Associate Professor in the Faculty of Applied Mathematics at AGH University of Science and Technology in Kraków, Poland. His interests include mathematical finance, financial modelling, computer-assisted proofs in dynamical systems and celestial mechanics. He has authored ten research publications, one book, and supervised over 30 MSc dissertations, mostly in mathematical finance.

Preface; 1. Risk and return; 2. Portfolios consisting of two assets; 3. Lagrange multipliers; 4. Portfolios of multiple assets; 5. The capital asset pricing model; 6. Utility functions; 7. Value at risk; 8. Coherent measures of risk; Index.