Lab 8 - Probability Lab The Problem: Purdue Property and...

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Probability Lab The Problem: Purdue Property and Casualty Co. (PP&C) sells, among other products, car insurance. Sue Purdue, a long standing customer, has had a claim in each of the last two years. Underwriting would like to know whether or not to cancel her insurance. An important piece of information: Underwriting doesn’t want to insure any one who has a greater than 1 in 10 chance of having a claim in any given year. Underwriting has asked the actuarial department to determine if 2 consecutive years of claims over the life of the policy is consistent with their underwriting standards, assuming a 40 year life for the policy. In other words, what is the chance of having 2 or more consecutive years with significant claims over a 40 year period, if the probability of a significant claim in a given year is 1/10. What about 3 or more? We will solve this problem two ways: experimentally and analytically. Such experimental solutions are called “Monte Carlo” solutions because of the famous casino at Monte Carlo. The Monte Carlo Solution: We will use the “Random Number Generation” function in Excel to generate a random sequence of 40, 0’s and 1’s, for which the 0 is 9 times more likely than the 1. We interpret this sequence as representing the accident record of one individual over a 40 year period, where each 1 represents a year in which there was a claim. This sequence represents a “bad record” if it has 2 or more consecutive 1’s anywhere. We will generate 20 such sequences and count the number of “bad records” found, which will give an estimate of the probability someone having a bad record. This process may also be used to estimate the probability of 3 or more consecutive bad years. The final result is shown on p. 4-5 below. In order to use the random number generator, you may need to apply the add-in. Click on the top left Excel button, then click on “Excel Opti ons” (first screen shot). Select “Add- Ins” from the left side. If “Analysis ToolPak” is located under Active Application Add- ins, you can click cancel. However, if “Analysis ToolPak” is located under Inactive Application Add-ins (as seen in the second screen shot), you will need to make sure the
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Lab 8 - Probability Lab The Problem: Purdue Property and...

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