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. 45 below.
In order to use the random number generator, you may need to apply the addin. 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 Addins (as seen in the second screen shot), you will need to make sure the
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 Spring '08
 Staff
 Probability, Randomness, random number, policy holders, monte carlo solution

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