Danika is the CEO of the startup companyDeepTrees, and she wants to insure the company's head office against theft. To this end, she has gathered the following 3 insurance offers:
1) The insurance companyNoRegretsoffers a comprehensive package that pays for any losses due to theft. The package costs $2,000 per year.
2) The insurance companyInsureNowoffers a cheaper package that only costs $1,500 per year, but the insurance holder has to pay the first $5,000 of any losses herself.
3) The insurance companyRiskIt, finally, offers an even cheaper package that only costs $1,000 per year. This package, however, only repays 75% of any potentially incurred losses.
Danika believes that the contents of the head office cost $15,000 to replace in case of a theft, and from local crime statistics she estimates that there is a 5% chance that the head office will be broken into in any given year. (You can assume that there is at most one theft in any given year.)
(a) In case of a theft, how much would Danika have to pay (i) under theNoRegrets package, (ii) theInsureNowpackage and (iii) the Risk It package?
(b) Construct a payoff table that models Danika's problem, and determine the optimal choice under the (i) maximin, (ii) maximax, (iii) maximum likelihood and (iv) expected value criterion.
(c) Which package would you choose? Justify your answer.