Some questions

Hi, I was wondering if anyone could help me with these questions:

1. Q&A Bank Part 2 Solutions Page 9


It says “Therefore, assuming that the lives are independent, then the variance is: 50000^2 X 0.014801 = 37002178”. Why do we need to make this assumption? Isn’t the calculation based on an individual policy?



2. Chapter 5 notes Page 63 middle



I don’t understand the part “d/dt (ln l(x+n) – ln l (x+t)) = mu (x+t)”



The formula I know is “mu (x) = - d/dt ln l (x) “. In the above equation, the “ d/dt ln l (x+n) “ should be equal to – mu (x+n), right?



3. Q&A Bank Part 1 Question 1.10 (ii)



I don’t understand the logic behind A 25:10**¬ > 0.3 because v ^ 10 = 0.38554 > 0.3. Can you please explain in more detail?



4. In the multiple state model, when I write out the symbol ‘nu’ how do I make it look different to the letter ‘v’?

 

Not as fare as yourself, so I'll attempt q2 about ch5.

thats from defn of tPx = l_(x+t) / l_(x)

when you take logs this becomes ln l_(x+t) - l_x

And as in this case we have
l_(x+n) - l_(x+t)

where the first l_(x+n) is constant with respect to t therefore differentiating removes this left with mu_(x+t)


hope this helps.

 

I am really bored at work, so I drew them for you. My nu is on the left and v is on the right. And by the way, the nu will normally have a x+t or something next to it, so there should be no confusion.

Erik.
View attachment nu.bmp

 

Hi ActStudent -
I agree with you on Q1, so can't help there.

Q3: I think what they're saying is that the worst that can happen for the financial value of the policy is that they stay alive and don't get their money for 10 yrs. If that is the case it's worth v^10, otherwise it's worth even more, so the EPV must be more than v^10>.3

L