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## Diff of /inst/ultimatead.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
+## 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
+
+## -*- 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
+## @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
+