1Risk
All situations with uncertainty involve, but not all situations with risk involve uncertainty
2Uncertainty
means we don’t know the probabilities associated with different outcomes
3Risk is necessary for uncertainty to exist, but uncertainty is not necessary for risk to exist
Ex: Flipping a fair coin is an event with risk (heads or tails) but no uncertainty (we know the probability of each potential outcome)
4Maximin Criterion
you would choose the option that maximizes the worst outcome.
This criterion avoids the worst possible outcomes!!!
“Choose the one with the least catastrophic
catastrophe
5Minimax-regret Criterion
focuses on relative outcomes
Ex: you would feel no regret if you refused insurance (since you got an A) but you would feel regret if you bought insurance (since you got a B). One measure of the size of the regret is the difference in utility between these outcomes (A vs. B)
6Expected Value
amount you should expect to win on average if you played the gamble in the long
run (if you played many many many times).
7Variance
measure for how widely dispersed
potential outcomes are in the gamble
8I flip a fair coin. If it lands heads, you receive $100. If it lands tails, you must pay $20
The average is (100+(−20))/2 = 80/2 = 40, which is also the expected value.
If outcomes are not equiprobable, average ≠ EV
9Actuarially Fair
a purchase if the price is equal to the expected value
Ex: Lottery, Assets, Insurance Policies
10Diminishing marginal utility of consumption
each unit of consumption provides less marginal utility than the previous unit
11Expected Utility Theory (EUT) Risk
In a situation that involves risk but no uncertainty,
we are able to construct expected value (EV) using the
probabilities of different outcomes and the “payouts” of
each possible outcome
12Expected Utility Theory
combines the use of utility functions to map outcomes (goods, services, money, etc.) into utility space with the concept of expected value for situations involving risk
13Theory of Choice
People have rational
preference orderings for goods and services,
which can be represented using indifference
curves and mapped into an ordinal “utility
space” using a utility function
14Expected Utility Example: I roll a fair die. You are paid $10*the number on the die
EV: $35
EU: 1/6 * sqrt 10+ 1/6 *sqrt 20+ 1/6 *sqrt 30+ 1/6 *sqrt 40+ 1/6 *sqrt 50+ 1/6
* sqrt60≈ 5.7
15risk loving
consumption [U(X) = X2]
16consumption [U(X) = X],
risk neutral
17risk averse
U(X) = X1/2 or ln(x)]
18Risk Averse risk perferences
• Diminishing marginal utility
• Concave utility function
• Don’t like variance
19Risk Averse risk perferences
• Constant marginal utility
• Linear utility function
• Don’t care about variance
20Risk Loving risk perferences
• Increasing marginal utility
• Convex utility function
• Prefer variance
21Certainty Equivalent
a certain amount of money that meets the following criteria:
– U(the gamble) = U(CE)