3. Finky faces a 80% chance of having a loss of $0 and a 20% chance of having a

Question

3. Finky faces a 80% chance of having a loss of $0 and a 20% chance of having a loss of $10.

Mitch also faces a 80% chance of having a loss of $0 and a 20% 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 $20

a. What is the actuarially fair premium (AFP) for Finky and Mitch? (1 point)

b. What is the actuarially fair premium (AFP) for Dan? (1 point)

c. If Dan is added to the risk pool for insurance, what would the expected loss (p*) be? (1 point)

d. Explain if the pool is still homogeneous or not. (1 point)

e. If the insurer charges all of them a price of $3, is that price a good deal for each of them? Why or why not? (hint - think about the AFP for each) (1 point)

Explanation / Answer

The actuarially fair premium is the premium that allows insurance company to exactly break even at zero profits. Where,

Profits = revenues - costs = premium -expected cost = 0

Therefore actuarially fair premium is equal to expected costs

Therefore,

Actuarially fair premium =p*(expected loss in first case) + (1-p) * (expected loss in second case)

a. Actuarially fair premium (AFP) for Finky and Mitch= 80% *($0)+ 20% *($10) = $2

b. The actuarially fair premium (AFP) for Dan = 80% *($0)+ 20% *($20) = $4

c. If Dan is added to the risk pool for insurance, what would the expected loss (p*) be

Expected loss (p*) = (2/3)* $2 + (1/3) * $4 = $2.67

d. Homogenous pool means that all have equal level of risk and risk pool should be large, otherwise people with lower risks will leave the pool to find another group which can raise the amount of expected loss. As the expected loss is not equal in this pool therefore the pool is not homogeneous.

e. If the insurer charges all of them a price of $3, that price a good deal for Dan as his expected loss is $4 but it is not a good deal for Finky and Mitch as their expected loss is only $2 so price of $3 is costly deal for them.

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