MS Module 23: Actuarial risk classification – homework assignment

(The attached PDF file has better formatting.)

Reading on discussion forum: Actuarial risk classification

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 balance principle, with

●    a base rate of 10
●    a starting relativity for column 1 of 1.8
●    a starting relativity for column 2 of 1.0

We use the following notation:

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 observed totals for each cell, row, and column?
B.    What are the formulas for each cell, row, and column using base rates and relativities?
C.    What is the equation to balance along Row 1?
D.    What is the implied relativity for Row 1, given the starting relativities by column?
E.    What is the equation to balance along Row 2?
F.    What is the implied relativity for Row 2, given the starting relativities by column?
G.    What is the equation to balance down Column 1?
H.    What is the implied relativity for Column 1, given the computed relativities by row?
I.    What is the equation to balance down Column 2?
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.)