Utility Theory

Question 1

Definition of a lottery

Answer 1

(X,p)

Question 2

Rational preferences

Answer 2

Complete and Transitive

Question 3

Axioms of EU

Answer 3

1) Continuity 2) Independence (adding arb third lottery doesnt shift ordering)

Question 4

Ordinal util

Answer 4

monotone

Question 5

Cardinal util

Answer 5

affine

Question 6

Jensens inequality

Answer 6

f concave, iff Ef(z)\leqf(Ez)

Question 7

Absolute risk aversion

Answer 7

Negative curvature, at wealth level

Question 8

Risk premium

Answer 8

payment to avoid risk

Question 9

Equivalent definitions of A is more risk averse than B (4 defin)

Answer 9

1) u_a concave of u_b; 2) aversion higher for all W; 3) risk premium higher; 5) certainty equivalence lower

Question 10

Certainty equivalence

Answer 10

Indifference between certainty and higher payment that has risk

Question 11

How does certainty equivalence relate to risk premium

Answer 11

C(w_0,\mu+x)=\mu-\pi_a(W,x)

Question 12

Arrow Pratt approximation for risk premium

Answer 12

\pi\approx 1/2A(w_0)Ey^2

Question 13

Write Arrow Pratt initial problem and FOC (what are you taking foc with respect to?)

Answer 13

Eu_A(w_0+kx)=u(W_0-g(k))

Question 14

Relative risk aversion

Answer 14

Abs times wealth

Question 15

FOSD

Answer 15

Y=X+eps where eps\leq0

Question 16

SOSD

Answer 16

higher var and lower mean