A firm owns two buildings which have the same value (W0 =40 for each building) a

Question

A firm owns two buildings which have the same value (W0 =40 for each building) and which are subjected to a risk of full loss with identical probability 1/4. Because these buildings are located far away from each other the risks are independent. The risk manager has a budget of 8 to spend on insurance premia in order to cover the risks. If he covers the first building at a coinsurance rate beta 1 = 0.6, which coinsurance rate will he obtain for building 2? What is the coinsurance rate identical for each building (i.e. beta = beta 1 = beta 2) that yields the same premium ? Show that whatever the total budget available a risk averter should always select beta 1 = beta 2. As usual, the proof is done by drawing the cumulative distributions of final wealth. This result illustrates the intuitive idea that one should "never gamble with one's insurance budget."

Explanation / Answer

a) Coinsurance of Building B

for building 1 and building 2

1 + 2 =1

0.6 +2 =1

2 =1-0.6 =0.4

b) The coninsurance rate identical for each building that yields the same premium

The coinsurance rate for each building is 50%

c) Whatever the total budget available the risk averter choose 1 = 2.

Coinsurance percentage (1) =[ (Amount of Coverage Purchased/ Property Value) * Loss ] * (Amount Payable + Deductible)

Coinsurance percentage (2) =[ (Amount of Coverage Purchased/ Property Value) * Loss ] * (Amount Payable + Deductible)

These both buildings have same employer and the similar worth together with similar premium. In this way. we can say that

Coinsurance percentage (1) = Coinsurance percentage (2)

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