CAS Exam 8 Fall 2017, Question 1

Study guide: Exam 8

An actuary has constructed a pure premium model using the Tweedie distribution with parameter $1 < p < 2$ to determine manual rates for a Workers' Compensation book of business. The output of the model is pure premium per $100 of payroll.

The following variables were considered for inclusion in the model:

Variable	Description or Source of Data	p-value
Industry	Construction, Manufacturing, All Other	0.002
Return to Work Program	Yes or No	0.008
Employee Age	Average Age in Years	0.003
Employee Tenure	Average Number of Years of Employment	0.005
Location	State of Jurisdiction	0.080
Employee Morale	Based on Results of Annual Company Survey	0.150
Number of Back Injuries	Supplied by Employer	0.010

The actuary has decided to use the following variables in the model: Industry, Employee Tenure, and Return to Work Program.

Part a (1.5 points)

Discuss the statistical and non-statistical considerations of including each of the three variables (Industry, Employee Tenure and Return to Work Program) in the model.

Part b (2 points)

Discuss the statistical and non-statistical considerations of excluding each of the remaining four variables (Employee Age, Location, Employee Morale and Number of Back Injuries) from the model.

Part c (1.5 points)

The actuary fits the log link GLM model using the three selected variables. Given the fitted model parameters below and the following information for a Manufacturing Workers' Compensation risk, calculate the standard premium for this risk for an annual policy period.

Parameter	Coefficient
Intercept	-0.631
Employee Tenure	-0.040
Return to Work Program: Yes	-0.200
Industry Type: Construction	0.350
Industry Type: All Other	-0.550

Data for Manufacturing Risk	Value
Payroll	$1,000,000
Employee Tenure	5 Years
Return to Work Program	No
Actual Losses for Experience Rating	$12,500
Fixed Expenses	$1,500
Variable Expenses (as % of premium)	20%
Experience Rating Constant (K)	$10,000

Part d (1.5 points)

The actuary has graphed actual vs. modeled expected loss ratios by size of risk for the company's entire Workers' Compensation book, which is shown below.

In order to improve the model fit for larger risks, the actuary is considering incorporating the variable "Latest 3 Year Historical Losses" into the model. Explain three reasons against doing so.

Part e (2 points)

The actuary is now developing a quote for a new Construction risk with $50,000,000 of payroll using this rating plan.

i. (1 point) Describe two potential issues in developing a premium for this risk under this rating plan.
ii. (1 point) Provide an alternative rating approach for this risk and briefly discuss the advantages of this alternative for the insured as well as the insurance company.

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