Finky faces a 70% chance of having a loss of $0 and a 30% chance of having a los
ID: 3053411 • Letter: F
Question
Finky faces a 70% chance of having a loss of $0 and a 30% chance of having a loss of $10.
Mitch also faces a 60% chance of having a loss of $0 and a 40% chance of having a loss of $10.
Dan faces a 80% chance of having a loss of $0 and a 20% chance of having a loss of $15
A. What is the actuarially fair premium (AFP) for Finky and Dan?
b. What is the actuarially fair premium (AFP) for Mitch?
c. If Mitch is added to the risk pool for insurance, what would the expected loss (p*) be?
d. Explain if the pool is still homogeneous or not.
Explanation / Answer
A)
AFP for Finky
AFP = $0*0.70 + 0.30 *$10= $3
AFP For Dan
AFP = $0*80 + 0.20*$15 =$ 3
B)
AFP for Mitch
AFP= $0*0.60 + $10*0.40 = $ 4
c)
If MItch is added to the risk pool for insurance
AFP = $ 4
and loss (1-p)=0.40
because 0.6 loss for $ 0
and 0.4 loss for $ 10
Then
1-0.6 = 0.4 loss for $0
1-0.4 = 0.6 loss for $10
d)
It is not homogenous for Mitch , Finky and Dan. As Finky and Mitch AFP is different from Mitch
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