I have been constructing some examples and I am finding cases where the
capital indicated by the expected policyholder deficit is negative! In
fact, if you give me some predetermined percentage of expected loss, I can
find a loss distribution that will give a negative surplus by this criteria.
Now we could debate whether or not my examples are realistic. But even if
they are not, this makes me wonder that if we can find some (perhaps
unrealistic) examples that are obviously wrong, are there realistic examples
that are 10%, 50% or even 100% wrong?
I would be extremely surprised if I was the first one to come up with such
Now consider the following two sets of actuaries. (1) The set of actuaries
who think the expected policyholder deficit is a good idea; and (2) The set
of actuaries who are aware of that the expected policyholder surplus can be
I suspect that there are a large number of actuaries in each set. I would
appreciate hearing from anybody in both of these sets on how they reconcile
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