Actuarial Outpost > Life Joint Mortality Equivalency
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#1
10-23-2012, 07:42 PM
 epshiple Member SOA Join Date: Mar 2012 Location: Phoenix Studying for MLC College: Arizona State University Posts: 42
Joint Mortality Equivalency

I am working on a project right now and have hit a wall on how to proceed. Product I am working on is a second to die product.

I have the qx's (probability of death in year x) for two single policies. I am wanting to show the equivalent qx of a joint policy comprised of the two individuals.

Note - I am not looking for the probability of the second death happening by year x, but rather on a year by year basis. So I want the probability that in year x the policy ends.

My best guess at the moment is to multiply the conditional probabilites of death for each person given that the other is dead.

Example - Person A and Person B

I take these two products and multiply them together and get what looks like a logical curve for the joint policy. It is always outside of the single policy curves, and it also meets up with the second curve once the first curve hits ultimate probability of death. Is there something I am missing in this computation?

Last edited by epshiple; 10-23-2012 at 08:03 PM..
#2
10-24-2012, 04:29 AM
 george24 Member SOA Join Date: Aug 2011 Studying for nothing Posts: 371

why not just the sum of 3 pieces:

both are alive, and then both die that year

that's assuming independence, but you'd probably want to factor in Lonely Heart Syndrome, etc.
#3
10-24-2012, 07:30 AM
 JMO Carol Marler Non-Actuary Join Date: Sep 2001 Location: Back home again in Indiana Studying for Nothing actuarial. Posts: 36,246

See article on page 4:
http://www.soa.org/library/newslette...h/act7803.aspx

And letters to the editor in this subsequent issue.
http://www.soa.org/library/newslette...e/act7806.aspx
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Last edited by JMO; 10-24-2012 at 07:36 AM..
#4
10-24-2012, 08:24 AM
 MathGeek92 Member Join Date: Jul 2004 Posts: 684

or.. just find out the Pxy and Pxy+1 and subtract the two... where Pxy is the probability that at least one is alive
#5
10-24-2012, 03:33 PM
 epshiple Member SOA Join Date: Mar 2012 Location: Phoenix Studying for MLC College: Arizona State University Posts: 42

I have taken a look at Frasier's method. Does this method work only with a joint policy comprised of identical age single policies?

If it does work among combinations of ages...

I have been transferring my results onto a graph to show the relationships of the two single policy mortality curves vs. the joint curve for the two and it just does not make sense to me that my joint line surpasses my single line at certain periods of time.

In other words, if I have person X, how is it that his probability of death is lower than person X joined with person Y for a joint policy. In the way I am looking at it, adding person Y should do nothing but decrease the likelihood of the policy ending, because now we need two people to die rather than just one. I have attached an excel sheet summarizing as I am not the best at describing the situation.

I understand the outside forces like broken heart syndrome, but my calculation should be treating it as if the two are independent. I want to understand that part before I move to bringing in dependencies between the two.
Attached Files
 Outpost Mortality.xlsx (47.5 KB, 145 views)
#6
10-24-2012, 06:10 PM
 Double High C Site Supporter Site Supporter SOA AAA Join Date: Sep 2001 Location: atop the 5th line above the staff Posts: 11,465

Quote:
 Originally Posted by epshiple I have taken a look at Frasier's method. Does this method work only with a joint policy comprised of identical age single policies?
No. It works in general, for 2 independent lives.

I didn't look at your file, but it was stated succintly in the quote below, but I added one clarification that may be your missing link:

Quote:
 Originally Posted by MathGeek92 or.. just find out the Pxy and Pxy+1 and subtract the two... where Pxy is the conditional probability that at least one is alive given that AT LEAST ONE - but maybe not two - was alive at the beginning of the prior year
(And of course, they were both alive at the issyue date.)

ICHP

All Fraser's method does is take a conditional probability, i.e. a weighted average of the probabilities of the three statuses.

Last edited by Double High C; 10-24-2012 at 06:16 PM..
#7
10-24-2012, 08:25 PM
 JoJo Member Join Date: Jan 2002 Posts: 1,438

An interesting read is the study on simultaneous deaths.

http://www.soa.org/search.aspx?searchterm="simultaneous%20death"

This study showed a whopping annual rate of .04 per 1000. I've seen lots of early duration COIs on survivorship policies that are way underpriced if the rate is really .04 per 1000.

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