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--- a +++ b/inst/ultimatead.m @@ -0,0 +1,66 @@ +## Copyright (C) 2009 Esteban Cervetto <estebancster@gmail.com> +## +## Octave is free software; you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation; either version 3 of the License, or (at +## your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +## General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## <http://www.gnu.org/licenses/>. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{ultimate} =} ultimatead (@var{s},@var{v}) +## Calculate the ultimate values by the Additive method. +## +## @var{s} is a mxn matrix that contains the run-off triangle, where m is the number of accident-years +## and n is the number of periods to final development. @var{s} may contain u = m-n complete years. +## The value @var{s}(i,k), 1<=i<=m, 0<=k<=n-1 represents the cumulative losses from accident-period i +## settled with a delay of at most k years. +## The values @var{s}(i,k) with i + k > m must be zero because is future time. +## @var{v} is an mx1 vector of known volume measures (like premiums or the number of contracts). +## +## The Additive method asumes that exists a development pattern on the incremental loss ratios (IRL). +## This means that the identity +## @group +## @example +## E[Z(i,k) ] +## IRL(k) = ------------ +## V(i) +## @end example +## @end group +## holds for all k = {0,...,n-1} and for all i = {1,...,m}. +## Z represents the incremental losses; then losses satisfy +## Z(k) = (S(k) - S(k-1) ),Z(0) = S(0) for all i = {1,...,m}. +## +## @var{ultimate} returns a column vector with the ultimate values. Their values are: +## @group +## @example +## @var{ultimate}(i) = ultimatecc(@var{s},@var{v},quotaad(@var{s},@var{v}))(i) +## @end example +## @end group +## It may be seen it match with the ultimate calculated by the Cape Cod Method. +## +## @seealso {bferguson, quotald, quotapanning} +## @end deftypefn + +## Author: Act. Esteban Cervetto ARG <estebancster@gmail.com> +## +## Maintainer: Act. Esteban Cervetto ARG <estebancster@gmail.com> +## +## Created: jul-2009 +## +## Version: 1.1.0 +## +## Keywords: actuarial reserves insurance bornhuetter ferguson chainladder + +function [ultimate] = ultimatead (S,V) + +ultimate = ultimatecc(S,V,quotaad(S,V)); + +end