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.)