Rik and Claire, a couple residing in Lincolnshire, own a house valued at 200,000. The probability...

 

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Rik and Claire, a couple residing in Lincolnshire, own a house valued at £200,000. The probability of a fire is p = 0.01. An insurance company offers insurance at a premium y per insured sum K. The couple's preferences can be represented by the utility function u(x) = x. If there is a fire, it will destroy the house and reduce its value to zero (we assume that the couple's land without a house has no value). (a) How large is the insurance premium at which the insurance company makes zero profit? (5 marks) (b) What is the couple's optimal choice of K if the insurance is actuarially fair, and how much wealth will they own in each state? (5 marks) Rik and Claire, a couple residing in Lincolnshire, own a house valued at £200,000. The probability of a fire is p = 0.01. An insurance company offers insurance at a premium y per insured sum K. The couple's preferences can be represented by the utility function u(x) = x. If there is a fire, it will destroy the house and reduce its value to zero (we assume that the couple's land without a house has no value). (a) How large is the insurance premium at which the insurance company makes zero profit? (5 marks) (b) What is the couple's optimal choice of K if the insurance is actuarially fair, and how much wealth will they own in each state? (5 marks)

Answer rating: 100% (QA)

Qa The insurance underwriter makes zero profit once the premium is up to the first moment of the payouts The first moment of the payouts is pK zero01200000 2000 Therefore the premium at that the corpo... View the full answer