Between zero and twelve months I assign -12 months the value for 12
months, zero months the value of zero, and 12 and 24 months the
selected value for 12 and 24 months. The results are usually
well-behaved, with the desired properties of convexity, continuity, and
equal slopes at end points. It will occasionally behave badly between
12 and 24 months with fast closing data, but so will other formula
interpolations (cubic spline and such). Defining the four data points
as u(-1), u(0), u(1) and u(2), the desired value as x and the fraction
of the year elapsed as s (and it's square as ss, and it's cube as sss),
the formula is:
x =3D u(-1) [-s/2 + ss - sss/2]
+ u(0) [ 1 - 5ss/2 + 3sss/2]
+ u(1) [s/2 + 2ss - 3sss/2]
+ u(2) [-ss/2 + sss/2]
Other formulas with different properties can be derived from the same
starting point, and formalas based on six or more data points are
available, but I don't think they add much.
Bill
lgariepy@rlicorp.com on 10/29/98 06:56:02 PM
To: casnet@lists.casact.org @ INTERNET
cc:
From: lgariepy@rlicorp.com
Date: 10/29/98 06:56 PM
Subject: Interpolation of Loss Development Factors
We are curretly reviewing our quarterly reserves evaluations. Since we
do not have historical quarterly data, we have used interpolation to
estimate other than 12, 24, 36, etc. LDFs. I am looking for better way
to estimate, especially for the most current accident year which has
less than 12 months of exposure and development.
Any suggestion?
Louis Gari=82py
lgariepy@rlicorp.com
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