You comment on the "lack of fit" of the collective risk model to Table M
is more interesting.
Several years ago I was analyzing a WC experience rating plan with data
that had the experience rating mod, and the total loss. From this data
I was able to estimate the probability of zero claims and concluded that
the negative binomial significantly understated this estimate.
Now in the new "Loss Models" by Klugman, Panjer and Willmot they discuss
compound claim count distributions which can be considerably more skewed
than the negative binomial. Also, they discuss modifying the
probability of zero claims. It would be interesting to see if you could
match Table M with these claim count distributions.
I have these compound claim count distributions into my aggregate loss
program. The process is described more fully at my web site
www.crimcalc.com.
Glenn Meyers
Insurance Services Office, Inc.
Internet: gmeyers@iso.com
Voice:(212) 898-5938
Fax: (212) 898-6060
----------
From: Lawn,Yin [SMTP:Yin.Lawn@cna.com]
Sent: Monday, June 29, 1998 2:57 PM
To: Meyers, Glenn G.; 'Lawn,Yin'
Cc: 'casnet@lists.casact.org'
Subject: RE: Discounting insurance charge in Table M
Glenn:
Thank you for your response. I am very aware of the program you
have
implemented.
Actually, my issue is not with the discounting of the insurance
charge
itself(like you said it is not a big issue now) but rather the
underlying parameters that was used in our(your?)aggregate loss
distribution function. In order to validate these assumptions
in the
aggregate loss distribution function, I have constructed an
aggregate
loss distribution functions implied by Table M and compare it to
the one
currently use. For unlimited loss limit, two aggregate loss
distribution functions seem to follow each other fairly close
except at
the extreme(high and low) entry ratios. This seems to be due to
the
nature of the distribution function used and there is nothing I
can do
to make it fit better. If I make it fits better at the low
entry ratio,
its fit at the high entry ratio will get worse and vice versa.
I think at the extreme entry ratios, it is probably not a good
idea to
use any loss distribution function to fit the aggregate loss
distribution(because it doesn't fit well at either very high and
very
low end). Instead, values from table M should be used.
However,
insurance charge generated from table M is not discounted which
is what
I am trying to accomplish. Thus, to sum up my question in one
sentence:
How to reflect time value of money using table M?
---Yin Lawn
----------
From: Meyers, Glenn G.
To: 'Lawn,Yin'
Cc: 'casnet@lists.casact.org'
Subject: RE: Discounting insurance charge in Table M
Date: Monday, June 29, 1998 8:01AM
Yin:
This was a big problem in the early eighties when interest rates
were in
the stratosphere. So called "paid loss retros" were common and
it seem
that since you get the retrospective premium later, you ought to
charge
more for the contract.
I addressed this problem by calculating an aggregate loss
distribution
at various settlement lags and calculated the expected
retrospective
premium at each lag. With this, you can calculate the present
value of
the retrospective premium, and adjust your insurance charge (or
other
plan factor) to get you the "right" present value.
I wrote up this in a paper titled "The Cash Flow of a
Retrospective
Rating Plan" which was published in the PCAS around 1986.
I was actually working for your company when I implemented this
and I
believe a PC version of these ideas is still being run by Brian
Montigney.
Glenn Meyers
Insurance Services Office, Inc.
Internet: gmeyers@iso.com
Voice:(212) 898-5938
Fax: (212) 898-6060
----------
From: Lawn,Yin [SMTP:Yin.Lawn@cna.com]
Sent: Friday, June 26, 1998 4:58 PM
To: casnet@lists.casact.org
Subject: Discounting insurance charge in Table M
Hi,
Does any body have any ideas(or articles and papers)on
how to
discount
insurance charge for time value of money? I don't think
current
table M
reflects time value of money associated with insurance
charge.
Is there
anyway to modify current procedure to obtain a
discounted excess
loss
ratio from table M? Maybe a formula for shifting column
just for
insurance charge discounting? Thanks.
---Yin Lawn
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