1- Decision making under risk/uncertainty Flashcards
Outline Risk & Uncertainty
-Risk is about random processes with known probabilities
-Uncertainty is for random processes with unknown probabilities
How can a lottery/gamble be expressed?
Action with probability weighted outcomes
aᵢ = [p₁cᵢ₁,…,pₘcᵢₘ]
What is the monotonicity axiom?
If there are 2 lotteries with the same random outcomes, the one with a higher probability is preferred
What is the Expected utility principle?
Choices should be made based on expected utility
What is the Neumann-Morgenstern utility function?
U(p) = Σpᵢuᵢ
Under what conditions does a utility function satisfy the expected utility property?
The independence axiom
Explain the Independence axiom
If indifferent between x and y, must also be indifferent between possibly receiving x or z and possibly receiving y or z (equal probabilities)
What is the Expected Utility Theorem?
If a set of lotteries and preferences satisfy independence and monotonicity axioms, then there’s a utility function that satisfies expected utility property
When are individuals risk averse?
If they prefer a fixed payment to a random payment of equal expected value
What is the Certainty equivalent?
The certain amount that makes someone indifferent between a risky payoff:
E(x) - π
What is the risk premium (π)?
The amount of EV below the uncertain payoff at which agents are indifferent
What 2 components is risk premium made of?
-Risk aversion factor (γ) (subjective)
-Market variability factor Var(x) (objective)
Describe the Arrow-Pratt measure of risk aversion (absolute risk aversion)
How much utility we gain as we add to our wealth
γ = -U’‘(E[x])/U’(E[x])
What is the relative risk aversion?
Absolute risk aversion times payoff
γx
Describe the intuition behind the Arrow-Pratt measure of absolute risk aversion (γ)
Measures the extent to which investors avoid risk as wealth increases
