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CT5 Sept 2014 Q13

Laura

Very Active Member
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!
 
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
 
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!
 
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