Actuarial Outpost > Life Testing for differences in mortality tables
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#1
08-23-2011, 09:59 AM
 mihairadu Join Date: Aug 2011 College: University of Amsterdam Posts: 4
Testing for differences in mortality tables

Hi all,

So the question is like this:
Suppose you have two mortality tables used to value your future CF for some life insurance portfolio.
When switching from one table to another (say in this case the switch was from a 2008 to a 2010 m. table) the liabilities increase with 340 mln euros.

What i am trying to develop at this moment:
- find a statistical test (measure) to say for a x% significance level if the increase/decrease in liabilities due to changes in mortality is significant.

In other words, how can i test/come up with a measure that has a known distribution having as input only two mortality tables ( with age, year of projection and prob. of survival as cells) and the known difference in liabilities?

I started with some simple formula or means of aggregation for the data as in

T = Sum_on_columns (Sum_of_rows (Xij-Yij)^2))
where Xij = cell values for first table
Yij = cell values for second table
and trying to find the distribution for this statistic.
Any clues on how to find this?

Thank you a lot for any input.
#2
08-24-2011, 03:08 AM
 AfterdarkMilan Join Date: Jan 2007 Posts: 23

I would most likely run a hypothesis tests (Kolmogorov-Smirnov, Anderson-Darling, and Chi-Square Test) on the mortality tables on some well-known parametric distributions for mortality and see from the results of the statistics which one is the best fit. There are some softwares that could test an overwhelming list of parametric distributions if you want an exhaustive study. Once I have fitted the mortality tables with a parametric distribution, everything will follow smoothly.
#3
08-25-2011, 04:28 AM
 mihairadu Join Date: Aug 2011 College: University of Amsterdam Posts: 4

Thanks for the idea - haven't thought of using a "brute force" approach.
Do you know any software that does this kind of testing?

I was trying to go for a smoother approach in the sense of trying to find the distribution for the test (or a variation of that test) that i wrote before (sum of squared differences).

Am I completely wrong when i say that if every data from the mortality table is obtained by using a projection model so basically every data point is actually drawn from a normal distribution with parameters u and sigma to be found out?

Still working on this path as i have no clue yet.
#4
08-25-2011, 08:07 AM
 JMO Carol Marler Non-Actuary Join Date: Sep 2001 Location: Back home again in Indiana Studying for Nothing actuarial. Posts: 37,660

I must confess I don't understand the point of your question. I could understand asking whether the change is MATERIAL (an accounting concept) for your company, but why do you want a statistical test? And what will you do with the answer when you get it?
Quote:
 Originally Posted by mihairadu Am I completely wrong when i say that if every data from the mortality table is obtained by using a projection model so basically every data point is actually drawn from a normal distribution with parameters u and sigma to be found out?
I don't think this is the way that mortality tables are created. They are based primarily on historic data, and there aren't any good, simple statistical models that fit.
You might do a search of the SOA site on "mortality table construction" although it may just point you to the appropriate text book.
There are some complex models that have been used in the past, although NOT for testing statistical significance. Do a search on Lee-Carter mortality models, for example.
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#5
08-25-2011, 11:31 AM
 mihairadu Join Date: Aug 2011 College: University of Amsterdam Posts: 4

The mortality tables are based on historical data indeed, over which a "projection model" is applied (e.g. fitting a Lee-Carter or Lee-Carter-Miller are the most common i believe).

The point of the question is quite simple: is the change in liabilities due to the change in mortality table values a plausible value?

And the test i am trying to create is just for my personal curiosity and desire to create something new - the problem could be well solved by comparing some plain graphs in Excel.

My first idea was to use some variation of a well known statistical test (as there are for contingency tables), develop that test based on the input data and find it's critical values.

I think in the end i will do it the famous Dickey-Fuller way - Monte Carlo all the way
#6
08-25-2011, 11:53 AM
 CuriousGeorge Member CAS SOA Join Date: Dec 2005 Posts: 1,339

Quote:
 Originally Posted by mihairadu The point of the question is quite simple: is the change in liabilities due to the change in mortality table values a plausible value?
How does finding out whether the tables are statistically different answer that question?

If I switch from a table that poorly correlates to actual experience, to one that is more closely related, whatever the change that arises is what it is. Knowing that the tables are different or similar doesn't make the change more or less plausible.
#7
08-25-2011, 11:58 AM
 mihairadu Join Date: Aug 2011 College: University of Amsterdam Posts: 4

This is exactly what i am trying to develop, not just the significance in the difference of the tables but also the impact on the liabilities.

Think of it as a version of a plain mean hypothetis testing.
You have u=350 the change in liabilities and you want to see if this change can be reasonably put on behalf of the change in mortality tables.

I am not discussing if the chosen mortality tables are correct or not, are close to reality or not, that is a different discussion.