## [677636]: inst / ultimatead.m Maximize Restore History

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### ultimatead.m    57 lines (52 with data), 2.3 kB

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56``` ```## Copyright (C) 2009 Esteban Cervetto ## ## 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 ## . ## -*- 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 ## ## @verbatim ## E[Z(i,k) ] ## IRL(k) = ------------ ## V(i) ## @end verbatim ## ## holds for all k = @{0, @dots{}, n-1@} and for all i = @{1, @dots{}, m@}. ## Z represents the incremental losses; then losses satisfy ## Z(k) = (S(k) - S(k-1) ),Z(0) = S(0) for all i = @{1, @dots{}, 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 function [ultimate] = ultimatead (S, V) ultimate = ultimatecc(S,V,quotaad(S,V)); end ```