An insurer uses classification ratemaking to set rates and uses a single rating variable to classify policies with three different levels: level I, level II and level III. The base level is level I. The pure premium for each level is assumed to be gamma distributed with unknown parameters [math]\theta [/math] and [math]\alpha [/math] that change across levels:

Level	[math]\alpha [/math]	[math]\theta [/math]	Exposure weight	Current rate differential
I	[math]\alpha_0[/math]	[math]\theta_0[/math]	40%	1
II	[math]2\alpha_0 [/math]	[math]\frac{2\theta_0}{3} [/math]	35%	1.25
III	[math]3\alpha_0 [/math]	[math]\frac{\theta_0}{2} [/math]	25%	1.6

If the insurer wants an overall rate increase of 10% and there are no fixed or variable expenses, determine, using the pure premium method, the rate change % for level III policies.

• +2.16%
• +2.78%
• +3.25%
• +3.78%
• +4.11%

The indicated rate differentials, based on the values of [math]\alpha [/math] and [math]\theta [/math] for each level, are given below:

Level [math]i[/math]	[math]R_{i,I} [/math]
I	1
II	4/3
III	3/2

Given a targeted overall change factor of 1.1, the indicated change factor for the base rate equals

[[math]] 1.1 \cdot \frac{\sum_i w_i R_{C,i}}{\sum_i w_i R_{I,i}} = \frac{1.36125}{1.2417} = 1.0963. [[/math]]

The change factor for level [math]i [/math] equals the change factor for the base level multiplied by the change factor of the indicated differential for level [math]i[/math]:

Level	Change Factor	Rate Change
I	1.0963	+9.63%
II	1.1694	+16.94%
III	1.0278	+ 2.78%