excans:8ab8dcffce: Difference between revisions
From Stochiki
mNo edit summary |
mNo edit summary |
||
| (One intermediate revision by the same user not shown) | |||
| Line 4: | Line 4: | ||
<div class="text-center"> | <div class="text-center"> | ||
{{#invoke_html:actuarial_science/pgram|html|700|300|70|4|7/1/3|11/15/5|10/1/6|7|-4|5}} | {{#invoke_html:actuarial_science/pgram|html|700|300|70|4|7/1/3|11/15/5|10/1/6|7|-4|5|pd=1}} | ||
</div> | </div> | ||
The upper left triangle for CY6 has area (1/2)(7/8)2 = 49/128 and the lower right triangle has area (1/2)(1/4)2 = 4/128. The weighted average is [49 + 4(1.008) + 75(0.960)]P/128 = 0.9768P. The current premium is 9200(1.008)/(0.9768) = 9494. | The upper left triangle for CY6 has area (1/2)(7/8)<sup>2 </sup>= 49/128 and the lower right triangle has area (1/2)(1/4)<sup>2 </sup>= 4/128. The weighted average is [49 + 4(1.008) + 75(0.960)]P/128 = 0.9768P. The current premium is 9200(1.008)/(0.9768) = 9494. | ||
{{soacopyright | 2023}} | {{soacopyright | 2023}} | ||
Latest revision as of 01:32, 8 August 2024
Key: C
Let P be the premium after the July 1, CY3 rate change. On November 15, CY5 the premium is 0.96P and on October 1, CY6 it becomes 1.05(0.96)P = 1.008P. The relevant parallelogram is:
The upper left triangle for CY6 has area (1/2)(7/8)2 = 49/128 and the lower right triangle has area (1/2)(1/4)2 = 4/128. The weighted average is [49 + 4(1.008) + 75(0.960)]P/128 = 0.9768P. The current premium is 9200(1.008)/(0.9768) = 9494.
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.