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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} =} ultimatecc (@var{s},@var{v},@var{quotas})
+## Calculate the ultimate values by the Cape Cod 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).
+## @var{quotas} is an 1xn vector of cumulatives quotas. 
+## 
+## The Cape Cod method asumes that exists a development pattern on the cumulative quotas (Q).
+## This means that the identity 
+## @group
+## @example
+##          E[S(i,k) ]
+## Q(k) = -------------
+##          E[S(i,n) ]
+## @end example
+## @end group
+## holds for all k = {0,...,n-1} and for all i = {1,...,m}.
+## 
+## Also, the Cape Cod Method asumes the existence of a value "H" in a way that satisfy
+## @group
+## @example
+##        S(i,n)
+## H = E [------]
+##         V(i)
+## @end example
+## @end group
+## holds for all i = {1,...,m}.
+## H is called the Cape Cod loss ratio and it can be prove this value is
+## @group
+## @example
+##                    j=n-1        
+##                     E   S(j,n-j)
+##                    j=0            
+## @var{quotas}(k) =  ----------------
+##                   j=n-1            
+##                     E   Q(n-j)V(j)
+##                    j=0             
+## @end example
+## @end group
+##
+## @var{ultimate} returns a row column with the ultimate values. Their values are:
+## @group
+## @example
+## @var{ultimate}(i) = H * @var{v}(i)
+## @end example
+## @end group
+##
+## @seealso {bferguson}
+## @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 = ultimatecc (S,V,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(V) ~= [m,1])
+ usage(strcat("volume V must be of size [",num2str(m),",1]" ));
+end  
+if (size(quotas) ~= [1,n])
+ usage("quotas must be of dimension [1,n]");
+end  
+
+# CapeCods K   K = S(i+k = n)/quotas*V
+
+if (u==0)
+K = sum(diag(fliplr(S))')/ (fliplr(quotas)*V);
+else
+K = sum([diag(fliplr(S),-u)' S(1:u,n)])/ (fliplr([quotas ones(u)])*V);
+end
+
+#ultimate value
+ultimate = K * V;
+
+end