Utility Theory Flashcards
Expected Utility
quantification of the DMs preferences towards an outcome under risk
Utility Curve
Utility is a function of reward U(r)
As the reward increases, the marginal utility gets smaller - Law of diminishing marginal return
Certain Monetary Equivalent
Guaranteed return that someone would accept now, rather than taking a chance on a higher, but uncertain, return in the future.
Types of Utility functions
Risk averse conditions
Risk taking conditions
Risk neutral conditions
Turning Point
Risk averse conditions (Utility function)
Concave
CME < EMV
Risk neutral conditions (Utility function)
Linear
CME = EMV
Risk Taking conditions (Utility function)
CME > EMV
Convex
Turning Point Condition (Utility function)
risk taking to a point then switch to risk averse
depends on the strategy you can afford
Prospect Theory
assumes that losses and gains are valued differently, and thus individuals make decisions based on perceived gains instead of perceived losses
Has a turning point
Insurance Problem
Insurance company and customer have varying opinions of risk
Creates a trading margin between the different CME values
Both CME < EMV
Von Neumann-Morganstern Axioms
Complete Ordering Continuity Independence Unequal Probability Compound Lottery
Complete Ordering Axiom
If r1 > r2
and r2 > r3
then r1 > r3
Continuity Axiom
for any gamble, there exists some probability such that the decision-maker is indifferent between the “best” and the “worst” outcome.
Independence Axiom
If a decision-maker is indifferent between two possible outcomes, then they will be indifferent between two lotteries which offer them with equal probabilities, if the lotteries are identical in every other way, i.e., the outcomes can be substituted
Allows the creation of simple lotteries from compounds
Given r1 and r2 are indifferent, you would then be indifferent between lottery with P(r1) and P(r3) and lottery with P(r2) and P(r3)
