What is a good introductory book on mathematical risk theory?

Question

I'm looking for a book that introduces the following concepts and illustrates them with examples and exercises:

• Risk measures (Value at Risk, Expected Shortfall, distortion risk measures, and more)
• (Modern) Portfolio theory
• Different notions of risk aversion (Arrow-Pratt and others)
• Utility functions (Von Neumann-Morgenstern)
• Stochastic orderings and stochastic dominance

And perhaps other important, related topics of which I am not aware. Do you know a good example of such a book?

Answer 1

Stochastic Finance. An Introduction in discrete time. by Foellmer and Schied gives an excellent introduction in chapters 2-4.

Answer 2

You can refer to Mathematical Methods in Risk Theory by Buhlmann. It has a very good selection and has some recent works in the mathematics of risk theory.

See also: Modern Actuarial Risk Theory by Kaas et.al. and Introduction to Mathematical Portfolio Theory by Joshi and Paterson.