Course 3 May 2001 #35

[boognish]

I was wondering why the common shock is included in the last to die Insurance, but not the insurances on (x) and (y) individually.

Typically in these types of problems you include common shock in both the individual insurances, and the joint insurances.

Thoughts???

[Cynic]

Read the question carefully. I don't have it in front of me, but from what I remember, the way the problem was stated already included the common shock mortality in each of the individual ones. That was why they used u* instead of u. But next time please post the question so people can follow.

[boognish]

You have calculated the actuarial pv of a last-survivor whole life insurance of 1on (x) and (y). You assumed:

i. the death ben. is payable at moment of death
ii. the future lifetimes of (x) and (y) are indep. , each life has a constant force of mortality with mu=.06
iii. delta=.05

Your supervisor points out that these are not indep future lifetimes. Each mortality assumption is correct, but each includes a commom shock with constant force .02

Calculate increase in actuarial present value over what you originally calculated.

See my original post......Thoughts????

[mopete]

that's right. the value of u(x) is unchanged after discovering the error.

so u(x) = 0.06 was the old assumption under independence

now, u(x) = u*(x) + u(shock) = 0.04 + 0.02 = 0.06


i think you're getting confused b/c you see that u(x) is unchanged, so you think they ignored the shock. they didn't --they just adjusted u*(x) so that when you include the shock (dependence) u(x) is the same. (that was stated in the question..."mortality assumption was correct").

note, this "adjustment" to u*(x) was done to both individual (Ax) and joint (Axy) insurances


Hope this helps. The solution should be easier to follow now I think.