Re: Interpolation of Loss Development Factors

Brad Gile ( (no email) )
Sun, 1 Nov 1998 19:13:26 -0600

There is an alternative to explicit interpolation formulae. For a given
Accident Year, let F(T) be the expected value of the ratio of (a) losses
paid (reported) to time T to (b) Ultimate losses, where time T is measure=
d
from the beginning of the Accident Year. using whatever you have for data=
,
get an estimate of F(T) as a known distribution and solve for the paramet=
ers
(I have found in the experience that I deal with, the WEIBULL distributio=
n
has done best) as a disribution for T). If T<1, then (Losses to Date)/(Fu=
ll
Year Ultimate) =3D F(T), and solve for Full Year Ultimate. If we assume t=
hat
losses are incurred uniformly over the year, then Incurred to T =3DT*Full=
Year
Ultimate. For other Accident Years, just use F(T) directly: Ultimate =3D
Losses to Date/F(T). One caveat on Reported Losses, though: they must be
fully developed to account for any case reserve biases!
Brad Gile

-----Original Message-----
From: vanarkb@towers.com <vanarkb@towers.com>
To: - (052)Casnet(a)lists.casact.org <Casnet@lists.casact.org>
Date: Sunday, November 01, 1998 6:48 PM
Subject: Re: Interpolation of Loss Development Factors

>Our life brothers and sisters have a variety of tools for "graduation"
>of data series, such as life tables organized in five year groups.
>Back in ancient times when I took exams, this was on their Part 5. (I
>learned it out of a study note by Greville, which clearly explained the
>mathematical underpinnings and tradoffs in such formalas.) I've gotten
>reasonable results using the Karup-King four point interpolation on
>inverted development factors (percent reported or percent paid,
>usually).
>
>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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