Asset Allocation and Portfolio Management Lec2

• (2.2):
  if the dom is not convex, then $\theta u+(1-\theta)$ may not be in the dom.

• f∗ is convex (even if f is not).

  See Theorem 2.4. Only ask it to be convex in y.

• Applications of Theorem 2.5: expg(x) is convex if g is convex. Also 1/g(x) is convex if g is concave and positive.

  Direct use of the theorem 2.5

• extended-value extension.

  Since we ask it to be $R\rightarrow R$. And it can’t be $-\infty$, since then it will lose minimum.

• The domain of a convex function is convex

  See (2.2), the definition.