
#1




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 (ADead*BDead) / [(ADead*BDead)+(ALives*BDead)] (BDead*ADead) / [(BDead*ADead) + (BLives*ADead)] 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; 10232012 at 08:03 PM.. 
#2




why not just the sum of 3 pieces:
both are alive, and then both die that year A is alive then dies, B is already dead B is alive then dies, A is already dead that's assuming independence, but you'd probably want to factor in Lonely Heart Syndrome, etc. 
#3




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
__________________
Carol Marler, ExActuary, Dedicated to Being Retired Just My Opinion: It's not an actuarial opinion; I'm no actuary, although I used to be one. My latest favorite quote, updated July 7, 2015 Last edited by JMO; 10242012 at 07:36 AM.. 
#4




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




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. 
#6




Quote:
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:
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; 10242012 at 06:16 PM.. 
#7




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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