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