Maciej J. Capiński 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. Ekkehard Kopp is Emeritus Professor of Mathematics at the University of Hull, where he taught courses at all levels in analysis, measure and probability, stochastic processes and mathematical finance between 1970 and 2007. His editorial experience includes service as founding member of the Springer Finance series (1998–2008) and the Cambridge University Press AIMS Library Series. He has taught in the UK, Canada and South Africa and he has authored more than 50 research publications and five books.

• 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.

Maciej J. Capiński 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. Ekkehard Kopp is Emeritus Professor of Mathematics at the University of Hull, where he taught courses at all levels in analysis, measure and probability, stochastic processes and mathematical finance between 1970 and 2007. His editorial experience includes service as founding member of the Springer Finance series (1998–2008) and the Cambridge University Press AIMS Library Series. He has taught in the UK, Canada and South Africa and he has authored more than 50 research publications and five books.

• 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.

Maciej J. Capiński 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. Ekkehard Kopp is Emeritus Professor of Mathematics at the University of Hull, where he taught courses at all levels in analysis, measure and probability, stochastic processes and mathematical finance between 1970 and 2007. His editorial experience includes service as founding member of the Springer Finance series (1998–2008) and the Cambridge University Press AIMS Library Series. He has taught in the UK, Canada and South Africa and he has authored more than 50 research publications and five books.

• 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.