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Diff of /inst/ultimateld.m [000000] .. [d39d4b] Maximize Restore

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+## 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} =} ultimateld (@var{s},@var{quotas})
+## Calculate the ultimate values by the Loss Development (Chainladder) 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. 
+## The 1xn vector @var{quotas} is a set of cumulative quotas calculated by some method.
+##
+## The LD method asumes that exists a development pattern on the individual factors.
+## This means that the identity 
+## @group
+## @example
+##             E[S(i,k) ]
+## LDI(k) =   -------------
+##            E[S(i,k-1) ]
+## @end example
+## @end group
+## holds for all k = {0,...,n-1} and for all i = {1,...,m}.
+##
+## This follows to 
+## @quotas
+## @example
+##                    l=n-1    1
+## @var{quotas}(k) =  II    -------
+##                    l=k+1  LDI(l) 
+## @end example
+## @end group
+## and the ultimate value is
+## @quotas
+## @example
+## @var{ultimate}(i) = @var{s}(i,n-i-1) / @var{quotas}(n-i-1)
+## @end example
+## @end group
+##
+## @seealso {bferguson, quotaad, 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 = ultimateld (S,quotas)
+
+[m,n] = size (S);           #triangle with m years (i=1,2,u,...u+1,u+2,....m) and n periods (k=0,1,2,...n-1)
+u = m - n;                                     #rows of the upper square
+S = fliplr(triu(fliplr(S),-u));                   #ensure S is triangular  
+
+if (size(quotas) ~= [1,n])
+ usage(strcat("quotas must be of size [1,",num2str(n),"]" ));
+end  
+
+#calculate the ultimate value
+
+if (u==0)
+ultimate = flipud(diag(fliplr(S))) ./ quotas';
+else
+ultimate = [(flipud(diag(fliplr(S),-u)) ./ quotas')', S(1:u,n)]';
+end
+ultimate = flipud(ultimate);
+
+end