With regards to Tutorial 4 question 5 2018, how can we equate a term contingent insurance with x=30, y=30 , n=30 to half of a joint life term assurance with x,y,n as above ?

Login

+2 votes

As the lives are identical \(x=30\) and \(y=30\), the term contingent assurance \(A_{\overset1{30}:30:30}\) is equivalent to \(\frac12a_{\overbrace{30:30}^1:30}\).

This is because the probability of either one dying first is equal (i.e. 1/2 each) as they are identical lives, and the joint life term assurance is the equivalent of a term contingent assurance on both lives, but with identical lives this leads to the equation as in question 5 of the tutorial.

The maths is as follows:

\(A_{\overbrace{30:30}^1:30}=A_{\overset1{30}:30:30}+A_{30:\overset1{30}:30}\)

But

\(A_{\overset1{30}:30:30}=A_{30:\overset1{30}:30}\)

as the lives are identical.

Hence

\(A_{\overbrace{30:30}^1:30}=2A_{\overset1{30}:30:30}\)

Hence

\(A_{\overset1{30}:30:30}=\frac12A_{\overbrace{30:30}^1:30}\)

- All categories
- BUS 1003H - Introduction to Financial Risk (52)
- BUS 2016H - Financial Mathematics (55)
- BUS 3018F - Models (74)
- BUS 3024S - Contingencies (61)
- BUS 4028F - Financial Economics (39)
- BUS 4027W - Actuarial Risk Management (54)
- BUS 4029H - Research Project (5)
- Mphil (1)
- Calculus and Pure Mathematics (4)
- Statistics (16)

...