## [d39d4b]: inst / quotaad.m  Maximize  Restore  History

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 ``` 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 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96``` ```## 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{quotas} =} quotaad (@var{s},@var{v}) ## Calculate the cumulative quotas 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{quotas} returns a row vector with the cumulative quotas. The transformation ## from incremental loss ratios to cumulative quotas is: ## @group ## @example ## l=k ## E IRL(l) ## l=0 ## @var{quotas}(k) = ----------- ## l=n-1 ## E IRL(l) ## l=0 ## @end example ## @end group ## ## @seealso {bferguson, quotald, quotapanning} ## @end deftypefn ## Author: Act. Esteban Cervetto ARG ## ## Maintainer: Act. Esteban Cervetto ARG ## ## Created: jul-2009 ## ## Version: 1.1.0 ## ## Keywords: actuarial reserves insurance bornhuetter ferguson chainladder function [quotas] = quotaad (S,V) [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 # Z triangle Z = [S(:,1), S(:,2:n)-S(:,1:n-1)]; Z = fliplr(triu(fliplr(Z),-u)); #clean Z # calc the empirical incremental loss ratios LRI = Z ./ repmat (V,1,n); #weights V(i)/sum(1,n-k,V(i)) W = repmat(V,1,n); #numerator W =fliplr(triu(fliplr(W),-u)); #clean low triangle a = repmat(sum(W),m,1); #denominator a = fliplr(triu(fliplr(a),-u)); #clean low triangle W = W./a; #divide by W = fliplr(triu(fliplr(W),-u)); # incremental Loss Ratios AD LRI_AD = diag(LRI' * W)'; #weighted product quotas = cumsum(porcentual(LRI_AD)); #calc cumulated quota end ```