Lecture 2

Question 1

Give the continuous representation of the vNM utility representation.

Answer 1

Question 2

Define the concept of first-order stochastic dominance given lotteries L and L’.

Answer 2

A lottery L first-order stochastically dominates L’ if for each x, the CDF of L is smaller than the CDF of L’. In effect, the probability of getting a prize less than a certain amount is always larger under L’.

Question 3

What is the relationship between Expectations and FOSD?

Answer 3

A lottery L FOSD L’ iff for each increasing utility function u, E[u(L)] >= E[u(L’)].

Question 4

Give the definition of a risk-averse agent.

Answer 4

[E[L]] prefered to L. I.e, the agent would prefer to get with certainty the expected prize of the lottery, raher than play the lottery itself.

Question 5

Give a proof of the link between risk aversion and concaveness of utility. (iff)

Answer 5

Question 6

Give three possible definitions of risk-aversion.

Answer 6

Question 7

Prove that all three definitions of risk aversion are equivalent.

Answer 7

Question 8

Give a proof of the relationship between FOSD and Expected utility.

Answer 8

Question 9

Provide a derivation of the Arrow Pratt measure of Risk Aversion

Answer 9

Slides 20-22

Question 10

leibnitz

Question 11

Integration by parts formula

Question 12

Define a Weak PBE

Answer 12