Decision Analysis 04(Oct 16)

Question 1

Differentiate deterministic and stochastic dominance.

Question 2

Differentiate between risk profiles and cumulative risk profiles.

Question 3

Full definition: Stochastic Dominance
* … Or
* If there is a probability space and random variables X’, and Y’ (in that space) with respective distribution functions FX(x) and FY(x) such that
Y’(ω) ≤ X’(ω) for all possible realizations ω. Or
*
* The second definition is useful but we need to have a method for generating associated random variables in the same probability space.
– The inverse transform method from simulation is useful

Answer 3

We say X is larger than Y with respect to usual stochastic order (Y ≤st X) if:
FX(x) ≤ FY(x) for all x.

If the inequality E[g(X)] ≥ E[g(Y)] holds for all increasing functions g