Chapter 18 question

[CHUN LEONG LEE]

Hello team. I have a question for the example given on page 18 of CS2 Chapter 18 (reinsurance)

For part c, at the bottom of the page 18 in the CMP, i am wondering how were the figures 0.329 and 1.24 derived please.

Thank you.

 

[CHUN LEONG LEE]

Also, one more question for page 21: how was the 6558^2 calculated / derived please.

Thank you.

 

[Andrew Martin]

Hello

Here we're interpolating between Phi(1.23) and Phi(1.24) to estimate Phi(1.23329). There are a few ways to write out the interpolation, all of which lead to the same result. My preferred method is to start with the following:

Phi(1.23329) ~= Phi(1.23) + (1.23329 - 1.23) / (1.24 - 1.23) * (Phi(1.24) - Phi(1.23))

This is saying that to estimate Phi(1.23329) (using linear interpolation), we need to travel the same proportion in the y direction as we do in the x direction, where that proportion is given by (1.23329 - 1.23) / (1.24 - 1.23).

Simplifying this we get:

Phi(1.23329) ~= Phi(1.23) + 0.00329 / 0.01 * (Phi(1.24) - Phi(1.23))
Phi(1.23329) ~= Phi(1.23) + 0.329 * (Phi(1.24) - Phi(1.23))
Phi(1.23329) ~= Phi(1.23) * (1 - 0.329) + 0.329 Phi(1.24)

Hope this helps!

Andy

 

[Andrew Martin]

Also, one more question for page 21: how was the 6558^2 calculated / derived please.

Thank you.

This is calculated in a separate question at the start of page 19.

Andy