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Anonymous
12-06-2001, 08:32 AM
Hi All!

I am getting confused with this percentile stuff. Which way do I calculate it?

Lets say - the 80th percentile -
a) .2 = tPx
OR
b) .8 = tPx

:???:

I have seen similar questions done both ways - or maybe I am reading this wrong? But how do I know what way to use?

THANKS!

Daisy
12-06-2001, 08:35 AM
80th percentile means only 20% of the population is "better" or "survives" therefore 80% must be dead by time t - so .20=tPx - hope that helps

Anonymous
12-06-2001, 08:49 AM
Yes, that does help - thanks Daisy!

Can I ask another question??? I am not too sure how to solve the following question.

Anyone wanna help?

A Whole life policy is issued to (30) with Z=10v^T 0<= T. If mu = 0.05 and the 80th percentile of Z is 5.12, find the APV of the benefit. The force of interest is constant. (ANS 2.5)

SO - where do I start? If I say .2 = tPx
and then Constant force gives me
0.2=e^(-mu*t)

NOW what? I don't understand since I am given mu and what the 80th percentile is? So, I want to find delta but how?

Thanks!

rabbit
12-06-2001, 09:30 AM
Since Z is biggest if the insured dies sooner (less time to discount the benefit payment), the 80th percentile of Z will actually occur at the 20th percentile of `time until death'. So you want to begin by solving 0.8 = tpx = e^(-mu * t). This gives
t = 4.4629.

Knowing the 80th percentile of Z is 5.12 tells us that 5.12 = 10*e^(-delta * t) which solves to give delta = 0.15.

Now, for constant force, the APV for a whole life policy with benefit of 1 is
(mu)/(mu + delta) = (0.05)/(0.2) = 0.25. So the benefit you are after is 10 * this amount, which is 2.5.

Anonymous
12-06-2001, 09:43 AM
Okay, but I don't like the first bit now! I follow through after but I don't see how you know to use .8 = tPx?

That was my initial problem - and found that for the 80th percentile, I want to say .2 = tPx not .8 = tPx.

So, I like everything but the first step. I don't know how I would know to do it that way? and how do you know it will occur at the 20th percentile?

I do appreciate your help.... THANKS and sorry I am a pain!

rabbit
12-06-2001, 09:50 AM
The way I remember it is that the sooner someone dies, the worse it is for the insurance company. Remember that the insurance company wants a small Z, since that is the PV of the death benefit. But a Z at the 80th percentile is a `big' Z (bigger than 80%, anyway).

Z is big when T is small. (Z is biggest if the insured dies right away.) So the 80th percentile of Z is at the 20th percentile for T.

It is a little confusing, and to be honest, my first attempt started with 0.2 = tpx also!

Hope this helps ....

Anonymous
12-06-2001, 11:04 AM
Thanks - that makes a bit more sense anyways. I will have to go through it a few times to get my head around it.

I think I need to keep my T's and Z's straight.