Uncertainty, Risk, and Insurance Flashcards
(16 cards)
What is a “state of the world” in uncertainty analysis?
A possible future scenario that might occur (e.g. “accident” or “no accident”); used to model outcomes under uncertainty.
What is a contingent consumption plan?
A bundle specifying consumption in each possible state of the world (e.g., wealth if a mishap occurs and if it doesn’t).
What is a state-contingent commodity?
A good that pays off in one specific state of the world (e.g., insurance payout only if a mishap occurs).
What is the general form of an expected utility function?
U(X,Y)=πxV(X)+πyV(Y)
Where X,Y are consumption in different states, 𝜋𝑥,𝜋𝑦 are probabilities, and
V(.) is the Bernoulli utility function.
How are risk preferences linked to the shape of V(.)?
Risk-averse:
V′′<0 (concave)
Risk-neutral:
V′′=0 (linear)
Risk-loving:
V′′ >0 (convex)
What is actuarially fair insurance?
Insurance where the expected payout equals the premium paid. That is, expected value of the contract = 0.
What does a risk-averse consumer do in the presence of actuarially fair insurance?
Fully insure — chooses a contingent plan with equal consumption in all states.
What is the tangency condition under expected utility?
MUx/MUy = πx/πy = Px/Py
What is the certainty line in insurance diagrams?
The 45° line Y=X — bundles on it yield the same consumption in both states (no risk).
How does the slope of the budget line relate to the premium?
Slope = 1−𝛾/𝛾, where 𝛾 is cost per £1 of coverage.
How does a risk-neutral consumer behave with actuarially fair insurance?
They are indifferent between insuring or not — utility depends only on expected income.
What does Jensen’s Inequality tell us about risk-averse consumers?
E[V(X)]<V(E[X])
A risk-averse person prefers the expected value of income to a risky income with the same expected value.
What’s the economic rationale behind diversification?
Reduces risk without reducing expected return — risk-averse agents prefer smoother (less variable) consumption across states.
In the example with Ice Cream Inc. and Umbrellas Inc., what is the optimal portfolio for a risk-averse investor?
Equal investment in both — yields £105 in both states (rain/sun), fully eliminating risk.
When will a consumer fully insure?
Preferences are risk-averse
Insurance is actuarially fair
Utility is smooth and concave in both states
