An insurance company will sell a fire insurance policy for a house similar to mi

Question

An insurance company will sell a fire insurance policy for a house similar to mine for $1000 (for one year of protection). If there is not a fire at my house this year, the insurance company has made a $1000 profit. Their experience indicates that there is a .001 probability that I will have a ‘total’ loss fire costing them $301,000 (meaning that they collected $1000 from me at the beginning of the year, and paid $301,000 to rebuild my home and replace loss contents during the year- a huge loss for them). There is a 1% chance that I’ll have a ‘small’ fire which will cause $41,000 in damages. Suppose that these are the only three possible outcomes in this simplified example.

The table below can be filled in to help answer the questions below.

Find the probability that the insurance company make a $1000 profit from the fire insurance policy that I buy for a given year.

Find the expected profit for the insurance company from the policy that I buy for a given year (the mean profit for mine and similar policies sold in a given year).

c)   Find the standard deviation for your variable.

d)   The mean shows that writing many fire insurance policies like this is good business for the insurance company, explain why.

e) The standard deviation provides some indication as to why it would be a bad idea for me to insure someone’s home myself in the same manner that the insurance company provides protection against financial loss from a fire. Explain why.

Explanation / Answer

Solution:-

a) The required probability = 1-0.001-0.01 = 0.989

b) Expected profit = 0.989*1000+0.001*(1000-301000)+0.01*(1000-41000)

= 989 + 0.001*(-300000) + 0.01(-40000)

= 989 - 300 - 400

= 989 - 700

= $289

c) Standard deviation = (0.989*(1000-289)^2+0.001*(1000-301000-289)^2+0.01*(1000-41000-289)^2)^0.5 = $10339.51

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