Modern portfolio theory

Introduction: In modern portfolio theory utility functions are used to describe the preferences of investors.

Definition: The utility function of an investor is given by $$U(\mu,\sigma)=\mu-\tfrac{1}{2}\alpha\sigma^2,$$ with
  • $\mu$ the expected return,
  • $\sigma \geq 0$ the corresponding risk,
  • $\alpha\geq 0$ the risk aversion coefficient of the investor.