Question

You own a house worth $400,000 that is located on a river. If the river floods moderately, the house will be completely destroyed. This happens once every 50 years. If you build a seawall, the river would have to flood heavily to destroy your house, which happens once every 200 years. What would be the annual premium for an insurance policy that offers full insurnace? For a policy that pays only 75% of the home value, what are your expected costs with and without the seawall? Do the different policies provide an incentive to be safer (i.e., to build a seawall)?

Answer 1

Value of House = $400,000

Expected loss with full insurance:

Without Sea wall = $400,000 * 1/50 = $8,000

With seawall, the expected loss would reduce to = $400,000 * 1/200 = $2,000

Insurance companies charge the expected loss as the premium for the insurance cover.

Expected loss with partial insurancce (75%)

The insurance cover would be for 400000 * 75% = $300,000

Expected loss without seawall = $300,000 * 1/50 = $6,000

Expected Loss with Seawall = $300,000 * 1/200 = $1,500

Insurance companies charge the expected loss as the premium for the insurance cover.

Expected cost each year will be :

Without Sea Wall = 0.02 * ($300,000 - $400,000) + 0.98 * (0) - $6,000= $ -8,000

With Sea Wall = 0.005 * ($300,000 - $400,000) + 0.995(0) - $1,500 = $-2,000

From the above calculations it is clear that in neither of the sitautions there is any benefit by taking or not taking any insurance cover. The expected loss and premium comes same. There can be only one option available for building seawall if the annual cost and maintenance is less than $6,000 a year.