Introduction to Mathematical Portfolio Theory

In this concise yet comprehensive guide to the mathematics of modern portfolio theory the authors discuss mean-variance analysis, factor models, utility theory, stochastic dominance, very long term investing, the capital asset pricing model, risk measures including VAR, coherence, market efficiency, rationality and the modelling of actuarial liabilities. Each topic is clearly explained with assumptions, mathematics, limitations, problems and solutions presented in turn. Joshi's trademark style of clarity and practicality is here brought to classical financial mathematics. The book is suitable for mathematically trained students in actuarial studies, business and economics as well as mathematics and finance, and it can be used for both self-study and as a course text. The authors' experience as both academics and practitioners brings clarity and relevance to the book, whilst ensuring that the limitations of models are highlighted.

Preface; 1. Definitions of risk and return; 2. Efficient portfolios: the two-asset case; 3. Portfolios with a risk-free asset; 4. Finding the efficient frontier – the multi-asset case; 5. Single-factor models; 6. Multi-factor models; 7. Introducing utility; 8. Utility and risk aversion; 9. Foundations of utility theory; 10. Maximising long-term growth; 11. Stochastic dominance; 12. Risk measures; 13. The Capital Asset Pricing Model; 14. The arbitrage pricing model; 15. Market efficiency and rationality; 16. Brownian motion and stock price models across time; Appendix A. Matrix algebra; Appendix B. Solutions; References; Index.

Mark S. Joshi is a researcher and consultant in mathematical finance, and a Professor at the University of Melbourne. His research focuses on derivatives pricing and interest rate derivatives in particular. He is the author of numerous research articles on quantitative finance and four books.
Jane M. Paterson obtained a PhD in pure mathematics from the University of Melbourne. She furthered her academic experience with a postdoctoral fellowship at the Mathematical Sciences Research Institute, Berkeley and a research fellowship at the University of Cambridge. More recently she has worked in both the UK and Australia as a director in a variety of specialist and generalist banking roles, including structured finance and economic capital, with organisations including National Australia Bank and ANZ.