02_Decision Making under Risk

Question 1

2 Main Methods for Decision Making under Risk

Answer 1

• Expected Utility Theory
• mu-sigma Rule

Question 2

Decision Situtation
under Risk

5 items

Answer 2

• multiiple scenarios with probabilities
• single goal
• single DM
• static decision context
• game against nature

Question 3

Certainty Equivalent
CE(L)

Answer 3

• Certainty Equivalent of a lottery L is the # CE(L) such that the DM is indifferent between the lottery and receivin a certain payement of CE(L)

Question 4

Risk Premium
RP(L)

Answer 4

• the Risk premium of a Lottery L is the difference between the expected value of the lottery EV(L) and the Certainty equivalent of the lottery CE(L)

Question 5

3 main types of utility functions

Answer 5

- linear
- convex (x^2)
- increase of utility is positive and increasing with x
- concave (x^0.5)
- increase of utility is positive and decreasing with x

Question 6

Arrow-Pratt Measure

Definition

Answer 6

• reveals the risk attitude of the DM at x

Question 7

3 different type of DMs

Answer 7

• risk averse
• risk seeking
• risk neutral

Question 8

Utility Function of
Risk Averse DM

Answer 8

• concave function

Question 9

Utility Function of
Risk Seeking DM

Answer 9

• convex function

Question 10

Utility Function of
Risk Neutral DM

Answer 10

• linear function

Question 11

What did Friedman and Savage (1948) observe regarding utility functions+

Answer 11

• utility function is mixed rather than only one type of utility function and depends on specific situation
• Situation I: Concave
• Situation II: Convex
• Situation III: Concave

Question 12

Standard deviation

mu-sigma rule

Answer 12

• sqrt of Variance

Question 13

Variance of the outcome of action a(i)

mu-sigma rule

Answer 13

[pj * e(i,j)^2] - EV(ai)^2

Question 14

mu(ai) / EV(ai)

mu-sigma rule

Answer 14

Sum of (e(i,j) * pj)

Question 15

Expected Utility
vs.
mu-sigma Rule

When will both rules lead to same decision?

Answer 15

in case of:
- risk neutral decision maker
- quadratic utility function and appropriate calibration of preference function
- normally distributed outcomes

Question 16

Drawbacks of mu-sigma rule

Answer 16

• does not guide the DM in calibrating the preference function
• cannot determine the risk attitude of the decision maker

Question 17

Decision Making under Risk
Criteria

5 items

Answer 17

• risk
• one criterion
• single DM
• static decision

Question 18

Arrow-Pratt Measure (AP)
Decision Rule regarding Risk Attitude

Answer 18

1. Risk Neutral
   AP(x) = 0
2. Risk Averse
   AP(x) > 0

3.Risk Seeking
AP(x) < 0

Question 19

Arrow-Pratt Measure
Formula

Answer 19

AP(x) = - [u’‘(x) / u’(x)]

Question 20

Risk Averse Attitude
- form of utility function
- CE(L) to EV
- RP(L)
- AP

Answer 20

• concave utility function
• CE < EV
• RP > 0
• AP > 0 as u’‘(x) < 0

Question 21

Risk Seeking Behaviour
- form of utility function
- CE(L)
- RP(L)
- AP

Answer 21

• convex utility function
• CE(L) > EV
• RP < 0
• AP < 0 as u’‘(x) > 0

Question 22

When can the expected value criterion be used for solving a decision problem? Characterize the decision context.

Answer 22

• risk
• single criterion
• Single risk neutral DM
• static
• randomly behavin opponent

Question 23

Which axioms must be satisfied for a DM to use expected utility criterion?

Answer 23

1. Complete Order
2. Continuity
3. Independence
4. Compound Lotteries
5. Unequal Probabilities