Section 10

 An insurance policy is a contract between the party that is at risk (the policyholder) and the insurer  The policyholder pays a premium to the insurer  In return the insurer reimburses certain claims to the policyholder  A claim is all or part of the loss, depending on contract

 Unless indicated otherwise, assume the amount paid to the policyholder is equal to the amount of the loss (“full insurance”)  The random variable X represents the amount of the loss  Don’t forget to include 0 as an outcome for X – if no loss occurs  E[X] is then the expected claim on the insurer  It is also called the pure premium – if no administrative or other costs are factored in, it would be how much the company asks for as a premium

These are less likely to appear on exam but relatively simple to remember, so it doesn’t hurt to know them

 This is just the application of what we learned in section 9  For example, if there are high, medium, and low classes of policyholders with different distributions, you may be asked to describe the distribution of a random loss from the portfolio

An insurance policy on an electrical device pays a benefit of 4000 if the device fails during the first year. The amount of the benefit decreases by 1000 each successive year until it reaches 0. If the device has not failed by the beginning of any given year, the probability of failure during that year is.4. What is the expected benefit under this policy?

An insurance policy is written to cover a loss, X, where X has a uniform distribution on [0,1000]. At what level must a deductible be set in order for the expected payment to be 25% of what it would be with no deductible?