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

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) The coinsurance rate indicates what will be paid by insurance company in case of loss once all the deductible have been met.

The cost of each building is 40 . The probability of full loss is 1/4. Hence, if risk manager covers the building with coinsurance rate of 0.6, then expected budget towards full loss is = 1/4 * 40*0.6

= 6

But, as he only has an available budget of 8, the risk manager can only afford to pay 2 towrds full loss of second building. The second building is also of 40 and probability of risk is 1/4. Hence, he will obtain coinsurance rate of 0.2 for second building

2) If the coinsurance of each building is 0.4, then risk manager can pay premium of 4 towards full loss of each building as each building costs 40 and probability of loss is 1/4.

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