CT5 Sept 2014 Q13

[Laura]

Hi, I'm having some trouble obtaining the dependent probabilities from the independent probabilities.

I obtain meu from each independent prob by meu=-ln(1-q_x)

Then I use the dependent prob formula.
However the numbers I obtain is slightly different e.g I get the following for the dependent prob of death for ages 55,56,57： 0.00473, 0.00593,0.00614
Which is different from the answer given.

Would you be able to explain how the answers in the examiner report are obtained?

Thanks!

 

[Joe Hook]

Hi Laura,

I haven't managed to reconcile your answers. You can get away with a couple of approaches here. Either you multiply the qxs by 110% or the forces of mortality.

With the former you would calculate mu55 as -ln(1-q55*1.1). Your dependent probability of death would then be:

mu55 / (mu55 + 0.04 + 0.1) * (1 - exp(-mu55 + 0.04 + 0.1)

With the latter you calculate mu as -ln(1-q55) and then multiply the resulting force by 110% to get mu55(*). This leads to a dependent probability of death of:

mu55(*) / (mu55(*) + 0.04 + 0.1) * (1 - exp(-mu55(*) + 0.04 + 0.1).

If this doesn't help, perhaps you could provide me with some more detailed calculations so I could see where things might have gone wrong.

Thanks
Joe

 

[Laura]

Hi Joe, I've just tried to calculate and managed to obtain the answers in the report - might have made some calculation mistakes somewhere previously.

Thanks Joe!