RA sproj on Attained Age, Tax Status, and Variable Annuity Withdrawal Rates
Actuaries use attained age to estimate mortality rates, injury rates, disability rates, claim frequencies, morbidity rates, and other pricing parameters. They use qualitative variables, such as sex, marital status, residence location, and cigarette smoking, or variables that may be either qualitative or quantitative, such as use of vehicle (which may include mileage), type of vehicle (which may include horsepower), credit status (for automobile insurance), and various medical indices (blood pressure, body mass index, cholesterol levels) for life insurance.
You can use your daily actuarial work as the data for your student project. Don’t put your company’s rate structure into your write-up and eliminate any sensitive data. Most items are not sensitive and can be used, perhaps with masking of actual figures. Check with your manager before doing the project.
Attained age is a good explanatory variable for many actuarial projects. As the first step in your student project, graph the dependent variable on the policyholder’s age.
If the graph seems linear, you can proceed to form regression equations.
If the graph seems exponential, you may use the logarithm of the dependent variable; this is useful for mortality rates, disability rates, and morbidity rates.
If the relevant ages start at an age above zero, such as age 16 for auto insurance or age 20 for life insurance, you may use Age – 16 or Age – 20. For auto insurance, you might use the logarithm of Age – 16. Graph the data on various scales to see what is closest to a linear relation.
Don’t be concerned if the true relation is not linear over the entire range of the independent variable. Use residual plots and dummy variables to separate ages into different groups.
Illustration: For auto insurance claim frequencies, you might use Age – 16. For ages 17 through 25, the regression parameter may be large (in absolute value); for ages 26 through 65, it may be small. Review the textbook chapter on dummy variables if you are not sure how to use them.
You can analyze the results for attained age of men vs women and then use an F test to see if a single regression equation would suffice (perhaps with a dummy variable for an age setback).
You might say: "These are well-known results." That is often true; the student project is not intended to prove new results.
Not all insurers keep the needed variables in easily accessible files. The age of the policyholder is kept on the original files, but may not be on the summary files to which you have access. Many insurers now have relational data bases with more data elements; each insurer is different.
The Society of Actuaries has published numerous inter-company studies with excellent data for student projects. Use the SOA web site to see the types of data which are available.