Insurance + Risk Aversion Flashcards
What is a Risky Prospect?
Set of Payoffs (W1, … , Wn)
- Each Payoff occurs w/ Prob. (p1, … , pn, ∑pi =1)
How can we Evaluate a Risky Prospect?
Calculating EU
EU = ∑ pi U(Wi)
What does a Risk Neutral person’s Utility look like?
Straight 45º Line - EU(L) = U [E(W)]
What does a Risk Averse person’s Utility look like?
Concave Utility Function
EU(L) < U [E(W)]
What does a Risk Loving person’s Utility look like?
Convex Utility Function
EU(L) > U [E(W)]
What is the Exp. Wealth?
E(W) = p(T - C) + (1 - p)T
= T - pC
What is the Exp. Utility of Wealth?
EU(W) = p U(T - C) + (1 - p) U(T)
What is the Utility of Exp. Wealth?
U [E(W)] = U(T - pC)
What 2 things does an Insurance Contract specify?
Compensation - Y
Premium - X
What is Compensation under Full Insurance and what level of Wealth does it provide?
Y = C
Certain Wealth : T - X
When is Full Insurance acceptable to a buyer?
S: U(S) = p U(T - C) + (1 - p) U(T) => S = Value that gives EU
F.I Acceptable: U(T - X) ≥ U(S)
When will a Risk Averse person NOT Buy Insurance?
If X > T - S
What Premium will an Insurance Company accept?
X ≥ pY
What is the Actuarially Fair Premium?
X = pY - due to Competition in Market
- Exp. Profits = 0
What are Fair Odds?
X = pY