## [5b02c4]: inst / ultimatecc.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``` ```## 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} =} 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 ## ## @verbatim ## E[S(i,k) ] ## Q(k) = ------------- ## E[S(i,n) ] ## @end verbatim ## ## holds for all k = @{0, @dots{}, n-1@} and for all i = @{1, @dots{}, m@}. ## ## Also, the Cape Cod Method asumes the existence of a value "H" in a way that satisfy ## ## @verbatim ## S(i,n) ## H = E [------] ## V(i) ## @end verbatim ## ## holds for all i = @{1, @dots{}, m@}. ## H is called the Cape Cod loss ratio and it can be prove this value is ## ## @verbatim ## j=n-1 ## E S(j,n-j) ## j=0 ## quotas(k) = ----------------- ## j=n-1 ## E Q(n-j)V(j) ## j=0 ## @end verbatim ## ## @var{ultimate} returns a row column with the ultimate values. Their values are: ## ## @verbatim ## ULTIMATE(i) = H * V(i) ## @end verbatim ## ## @seealso {bferguson} ## @end deftypefn 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 ```