By NEAS - 6/30/2024 1:21:20 PM
MS Module 24: Actuarial risk classification – homework assignment
(The attached PDF file has better formatting.)
Homework assignment
The mean values and the number of observations in each cell of a 2 × 2 classification table are
Means Column 1 Column 2 Observations Column 1 Column 2
Row 1 20 12 Row 1 5 4
Row 2 8 3 Row 2 2 3
Illustration: The cell in row 1 column 1 has a mean of 20 from a sample of 5 observations.
An actuary is setting class relativities for insurance pricing using a multiplicative model and a least squares bias function with
● a base rate of 4
● a starting relativity for column 1 of 2.0
● a starting relativity for column 2 of 1.0
We use the following notation:
Mjk = mean value for the cell with row j and column k
Njk = number of observations for the cell with row j and column k
B = base rate
r1 = relativity for Row 1
r2 = relativity for Row 2
c1 = relativity for Column 1
c2 = relativity for Column 2
A. What are the squared errors in each cell?
B. What is the mean squared error?
C. What is the partial derivative equation for the Row 1 relativity?
D. What is the implied relativity for Row 1, given the starting relativities by column?
E. What is the partial derivative equation for the Row 2 relativity?
F. What is the implied relativity for Row 2, given the starting relativities by column?
G. What is the partial derivative equation for the Column 1 relativity?
H. What is the implied relativity for Column 1, given the computed relativities by row?
I. What is the partial derivative equation for the Column 2 relativity?
J. What is the implied relativity for Column 2, given the computed relativities by row?
(The homework assignment has a format similar to that of the practice problem for this module, though the figures in each cell differ.)
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