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From: <hauberg@us...>  20090725 17:44:58

Revision: 6050 http://octave.svn.sourceforge.net/octave/?rev=6050&view=rev Author: hauberg Date: 20090725 17:44:47 +0000 (Sat, 25 Jul 2009) Log Message:  Minor documentation error (from Dr.Ing. Torsten Finke) Modified Paths:  trunk/octaveforge/main/signal/inst/idct.m Modified: trunk/octaveforge/main/signal/inst/idct.m ===================================================================  trunk/octaveforge/main/signal/inst/idct.m 20090725 14:46:47 UTC (rev 6049) +++ trunk/octaveforge/main/signal/inst/idct.m 20090725 17:44:47 UTC (rev 6050) @@ 23,7 +23,7 @@ ## The inverse discrete cosine transform x of X can be defined as follows: ## ## N1 ## x[n] = sum w(k) X[k] cos (pi (2n+1) k / 2N ), k = 0, ..., N1 +## x[n] = sum w(k) X[k] cos (pi (2n+1) k / 2N ), n = 0, ..., N1 ## k=0 ## ## with w(0) = sqrt(1/N) and w(k) = sqrt(2/N), k = 1, ..., N1 This was sent by the SourceForge.net collaborative development platform, the world's largest Open Source development site. 
From: <esteban319@us...>  20090725 14:46:55

Revision: 6049 http://octave.svn.sourceforge.net/octave/?rev=6049&view=rev Author: esteban319 Date: 20090725 14:46:47 +0000 (Sat, 25 Jul 2009) Log Message:  Added Paths:  trunk/octaveforge/main/actuarial/ trunk/octaveforge/main/actuarial/COPYING trunk/octaveforge/main/actuarial/DESCRIPTION trunk/octaveforge/main/actuarial/INDEX trunk/octaveforge/main/actuarial/inst/ trunk/octaveforge/main/actuarial/inst/bfanalisis.m trunk/octaveforge/main/actuarial/inst/bferguson.m trunk/octaveforge/main/actuarial/inst/quotaad.m trunk/octaveforge/main/actuarial/inst/quotald.m trunk/octaveforge/main/actuarial/inst/quotamack.m trunk/octaveforge/main/actuarial/inst/quotapanning.m trunk/octaveforge/main/actuarial/inst/ultimatead.m trunk/octaveforge/main/actuarial/inst/ultimatecc.m trunk/octaveforge/main/actuarial/inst/ultimateld.m trunk/octaveforge/main/actuarial/inst/ultimatemack.m trunk/octaveforge/main/actuarial/inst/ultimatepanning.m Added: trunk/octaveforge/main/actuarial/COPYING ===================================================================  trunk/octaveforge/main/actuarial/COPYING (rev 0) +++ trunk/octaveforge/main/actuarial/COPYING 20090725 14:46:47 UTC (rev 6049) @@ 0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>; + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. 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Added: trunk/octaveforge/main/actuarial/DESCRIPTION ===================================================================  trunk/octaveforge/main/actuarial/DESCRIPTION (rev 0) +++ trunk/octaveforge/main/actuarial/DESCRIPTION 20090725 14:46:47 UTC (rev 6049) @@ 0,0 +1,17 @@ +Name: Actuarial +Version: 1.1.0 +Date: 20090723 +Author: Act. Esteban Cervetto ARG <estebancster@...> +Maintainer: Act. Esteban Cervetto ARG <estebancster@...> +Title: Actuarial. +Description: Actuarial functions for Casualty and Property lines. +Depends: octave (>= 3.0.1) +Autoload: yes +License: GPL version 2 or later +Url: http://octave.sf.net +#I am an Actuary from Argentina. +#If you are looking for an Actuary +#If you are an idea to develop +#if you only want to talk about the actuarial career +#email me please. +#Actually, I speak Spanish. Added: trunk/octaveforge/main/actuarial/INDEX ===================================================================  trunk/octaveforge/main/actuarial/INDEX (rev 0) +++ trunk/octaveforge/main/actuarial/INDEX 20090725 14:46:47 UTC (rev 6049) @@ 0,0 +1,13 @@ +actuarial >> Actuarial +Actuarial + bfanalisis + bferguson + quotald + quotamack + quotaad + quotapanning + ultimateld + ultimatead + ultimatemack + ultimatecc + ultimatepanning Added: trunk/octaveforge/main/actuarial/inst/bfanalisis.m ===================================================================  trunk/octaveforge/main/actuarial/inst/bfanalisis.m (rev 0) +++ trunk/octaveforge/main/actuarial/inst/bfanalisis.m 20090725 14:46:47 UTC (rev 6049) @@ 0,0 +1,163 @@ +## Copyright (C) 2009 Esteban Cervetto <estebancster@...> +## +## 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{quotas}, @var{outcome} =} bfanalisis (@var{S}, @var{V}, @var{quota_ext}, @var{ultimate_ext}) +## Calculate the extended BornhuetterFerguson method for reserves in many ways. If all arguments are provided, +## it calculates 30 different estimations included in the @var{outcome} structure. It also returns the @var{quotas} used. +## +##@var{outcome} had two levels: +## +##@group +##level 1: Type of Ultimate +## list of posible estimative methods: +##@example +##@multitable {xxxxxxxxxxxxx} {xxxxxxxxxxxxxxxxxx} {xxxxxxxxxxxxx} {xxxxxxxxxxxxxxxxx} +##@headitem FLAG @tab METHOD @tab REQUIRES @tab RELATED FUNCTION +##@item ultad @tab Loss Ratio AD @tab S,V @tab ultimatead.m +##@item ultcc @tab Cape Cod @tab S,V @tab ultimatecc.m +##@item ultexternal @tab none @tab ultimate_ext @tab none +##@item ultld @tab Loss Development @tab S @tab ultimateld.m +##@item ultmack @tab Mack @tab S,V @tab ultimatemack.m +##@item ultpanning @tab Panning @tab S @tab ultimatepanning.m +##@end multitable +##@end example +##@end group +##@group +##level 2: Type of Quotas +## list of posible estimative methods: +##@example +## +##@multitable {xxxxxxxxxxxxxxxx} {xxxxxxxxxxxxxxxxxx} {xxxxxxxxxxxxx} {xxxxxxxxxxxxxxxxxx} +##@headitem FLAG @tab METHOD @tab REQUIRES @tab RELATED FUNCTION +##@item quotasad @tab Loss Ratio AD @tab S,V @tab quotaad.m +##@item quotasexternal @tab none @tab quota_ext @tab none +##@item quotasld @tab Loss Development @tab S @tab quotald.m +##@item quotasmack @tab Mack @tab S,V @tab quotamack.m +##@item quotaspanning @tab Panning @tab S @tab quotapanning.m +##@end multitable +##@end example +##@end group +## +## Parameters: +## @var{S} is a mxn matrix that contains the runoff triangle, where m is the number of accidentyears +## and n is the number of periods to final development. @var{s} may contain u = mn complete years. +## Optional: +## @var{v} is an mx1 vector of known volume measures (like premiums or the number of contracts). +## @var{quota_ext} is an 1xn vector with an external scheme of quotas. +## @group +## @example +## +## E[S(i,k+1)] +## quota(k) = , k={0,1,n1} +## E[S(i,n) ] +## +## @end example +## @end group +## @var{ultimate_ext} is a mx1 vector wuth an external estimatios of the ultimate column. +## +## +## @seealso {bferguson} +## @end deftypefn +## @bye + +## Author: Act. Esteban Cervetto ARG <estebancster@...> +## +## Maintainer: Act. Esteban Cervetto ARG <estebancster@...> +## +## Created: jul2009 +## +## Version: 1.1.0 +## +## Keywords: actuarial reserves insurance bornhuetter ferguson chainladder + +function [quotas,outcome] = bfanalisis (S,V,quota_ext,ultimate_ext) + +#check number of arguments in +if (nargin==0) + usage("insuficient args. Enter a mxn triangle of losses at least"); +else + #check S + [m,n] = size (S); #triangle with m years (i=1,2,u,...u+1,u+2,....m) and n periods (k=0,1,2,...n1) + u = m  n; #rows of the upper square + S = fliplr(triu(fliplr(S),u)); #ensure S is triangular + quotas.ld = quotald(S); #quotas LD + quotas.panning = quotapanning(S); #Panning quotas + for k=1:n + outcome.ultld.quotasld(:,k) = bferguson(S,quotas.ld,ultimateld(S,quotas.ld),k1); + outcome.ultld.quotaspanning(:,k) = bferguson(S,quotas.panning,ultimateld(S,quotas.panning),k1); + outcome.ultpanning.quotasld(:,k) = bferguson(S,quotas.ld,ultimatepanning(S,quotas.ld),k1); + outcome.ultpanning.quotaspanning(:,k) = bferguson(S,quotas.panning,ultimatepanning(S,quotas.panning),k1); + endfor + + if (nargin>1) + # verify V + if (size(V) ~= [m,1]) + usage(strcat("volume V must be of size [",num2str(m),",1]" )); + else + for k=1:n + quotas.ad = quotaad(S,V); #quotas AD + quotas.mack = quotamack(S,V); #quotas Mack + outcome.ultld.quotasad(:,k) = bferguson(S,quotas.ad,ultimateld(S,quotas.ad),k1); + outcome.ultld.quotasmack(:,k) = bferguson(S,quotas.mack,ultimateld(S,quotas.mack),k1); + outcome.ultpanning.quotasad(:,k) = bferguson(S,quotas.ad,ultimatepanning(S,quotas.ad),k1); + outcome.ultpanning.quotasmack(:,k) = bferguson(S,quotas.mack,ultimatepanning(S,quotas.mack),k1); + outcome.ultad.quotasld(:,k) = bferguson(S,quotas.ld,ultimatead(S,V),k1); + outcome.ultad.quotaspanning(:,k) = bferguson(S,quotas.panning,ultimatead(S,V),k1); + outcome.ultad.quotasad(:,k) = bferguson(S,quotas.ad,ultimatead(S,V),k1); + outcome.ultad.quotasmack(:,k) = bferguson(S,quotas.mack,ultimatead(S,V),k1); + outcome.ultcc.quotasld(:,k) = bferguson(S,quotas.ld,ultimatecc(S,V,quotas.ld),k1); + outcome.ultcc.quotaspanning(:,k) = bferguson(S,quotas.panning,ultimatecc(S,V,quotas.panning),k1); + outcome.ultcc.quotasad(:,k) = bferguson(S,quotas.ad,ultimatecc(S,V,quotas.ad),k1); + outcome.ultcc.quotasmack(:,k) = bferguson(S,quotas.mack,ultimatecc(S,V,quotas.mack),k1); + outcome.ultmack.quotasld(:,k) = bferguson(S,quotas.ld,ultimatemack(S,V),k1); + outcome.ultmack.quotaspanning(:,k) = bferguson(S,quotas.panning,ultimatemack(S,V),k1); + outcome.ultmack.quotasad(:,k) = bferguson(S,quotas.ad,ultimatemack(S,V),k1); + outcome.ultmack.quotasmack(:,k) = bferguson(S,quotas.mack,ultimatemack(S,V),k1); + endfor + if (nargin>2) + #check out quota_ext + if (size(quota_ext) ~= [1,n]) + usage(strcat("quota_ext must be of size [1,",num2str(n),"]" )); + else + for k=1:n + quotas.external = quota_ext; #external quotas + outcome.ultld.quotasexternal(:,k) = bferguson(S,quotas.external,ultimateld(S,quotas.external),k1); + outcome.ultpanning.quotasexternal(:,k) = bferguson(S,quotas.external,ultimatepanning(S,quotas.external),k1); + outcome.ultad.quotasexternal(:,k) = bferguson(S,quotas.external,ultimatead(S,V),k1); + outcome.ultcc.quotasexternal(:,k) = bferguson(S,quotas.external,ultimatecc(S,V,quotas.external),k1); + outcome.ultmack.quotasexternal(:,k) = bferguson(S,quotas.external,ultimatemack(S,V),k1); + endfor + if (nargin>3) + #verify ultimate_ext + if (size(ultimate_ext) ~= [m,1]) + usage(strcat("ultimate_ext must be of size [",num2str(m),",1]" )); + else + for k=1:n + outcome.ultexternal.quotasld(:,k) = bferguson(S,quotas.ld,ultimate_ext,k1); + outcome.ultexternal.quotaspanning(:,k) = bferguson(S,quotas.panning,ultimate_ext,k1); + outcome.ultexternal.quotasad(:,k) = bferguson(S,quotas.ad,ultimate_ext,k1); + outcome.ultexternal.quotasmack(:,k) = bferguson(S,quotas.mack,ultimate_ext,k1); + outcome.ultexternal.quotasexternal(:,k) = bferguson(S,quotas.external,ultimate_ext,k1); + endfor + end + end + end + end + end +end + +end Added: trunk/octaveforge/main/actuarial/inst/bferguson.m ===================================================================  trunk/octaveforge/main/actuarial/inst/bferguson.m (rev 0) +++ trunk/octaveforge/main/actuarial/inst/bferguson.m 20090725 14:46:47 UTC (rev 6049) @@ 0,0 +1,75 @@ +## Copyright (C) 2009 Esteban Cervetto <estebancster@...> +## +## 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{BF} =} bferguson (@var{s}, @var{quotas}, @var{ultimate}, @var{k}) +## Calculate the extended BornhuetterFerguson method for reserves. +## @var{BF} provides a column vector with the elements of @var{k}th period of development. +## @var{s} is a mxn matrix that contains the runoff triangle, where m is the number of accidentyears +## and n is the number of periods to final development. @var{s} may contain u = mn complete years. +## @var{k} may vary from 0 (first period) to n1 (final period). +## +## The BornhuetterFerguson predictors of the losses S(i,@var{k}) with i + @var{k} > n are defined as +## @tex +## @example +## @group +## $$ +## S _{i,k}^BF (hat %gamma, hat %alfa) = S _{i,ni} + (%gamma_{k}  %gamma_{ni})%alfa_{i} +## $$ +## @end group +## @end example +## @end tex +## @ifnottex +## @example +## @group +## S(i,@var{k})= S(i,ni)+ (@var{quotas}(@var{k}) @var{quotas}(ni))* @var{ultimate}(i) +## @end group +## @end example +## @end ifnottex +## +## @seealso {bfanalysis} +## @end deftypefn + +## Author: Act. Esteban Cervetto ARG <estebancster@...> +## +## Maintainer: Act. Esteban Cervetto ARG <estebancster@...> +## +## Created: jul2009 +## +## Version: 1.1.0 +## +## Keywords: actuarial reserves insurance bornhuetter ferguson chainladder + + +function [BF] = bferguson (S, quotas,ultimate,k) + +[m,n] = size (S); #triangle with m years (i=1,2,u,...u+1,u+2,....m) and n periods (k=0,1,2,...n1) +if (size(quotas) ~= [1,n]) + usage(strcat("quotas must be of size [1,",num2str(n),"]" )) +end +if (size(ultimate) ~= [m,1]) + usage(strcat("ultimate must be of size [",num2str(m),",1]" )) +end + +u = m  n; #rows of the upper square +S = fliplr(triu(fliplr(S),u)); #ensure S is triangular +diagS = diag(fliplr(S),u); + +#calcs the proyection by the bornhuetterferguson method +BF = diagS((nk+1):n,1) + (quotas(k+1)*ones(1,k)  quotas(k:1:1))' .* ultimate((mk+1):m); +BF = [S(1:mk,k+1); BF]; + +end Added: trunk/octaveforge/main/actuarial/inst/quotaad.m ===================================================================  trunk/octaveforge/main/actuarial/inst/quotaad.m (rev 0) +++ trunk/octaveforge/main/actuarial/inst/quotaad.m 20090725 14:46:47 UTC (rev 6049) @@ 0,0 +1,96 @@ +## Copyright (C) 2009 Esteban Cervetto <estebancster@...> +## +## 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{quotas} =} quotaad (@var{s},@var{v}) +## Calculate the cumulative quotas by the Additive method. +## +## @var{s} is a mxn matrix that contains the runoff triangle, where m is the number of accidentyears +## and n is the number of periods to final development. @var{s} may contain u = mn complete years. +## The value @var{s}(i,k), 1<=i<=m, 0<=k<=n1 represents the cumulative losses from accidentperiod 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,...,n1} and for all i = {1,...,m}. +## Z represents the incremental losses; then losses satisfy +## Z(k) = (S(k)  S(k1) ),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=n1 +## E IRL(l) +## l=0 +## @end example +## @end group +## +## @seealso {bferguson, quotald, quotapanning} +## @end deftypefn + +## Author: Act. Esteban Cervetto ARG <estebancster@...> +## +## Maintainer: Act. Esteban Cervetto ARG <estebancster@...> +## +## Created: jul2009 +## +## 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,...n1) +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:n1)]; +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,nk,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 Added: trunk/octaveforge/main/actuarial/inst/quotald.m ===================================================================  trunk/octaveforge/main/actuarial/inst/quotald.m (rev 0) +++ trunk/octaveforge/main/actuarial/inst/quotald.m 20090725 14:46:47 UTC (rev 6049) @@ 0,0 +1,83 @@ +## Copyright (C) 2009 Esteban Cervetto <estebancster@...> +## +## 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{quotas} =} quotald (@var{s}) +## Calculate the cumulative quotas by the Loss Development (Chainladder) method. +## +## @var{s} is a mxn matrix that contains the runoff triangle, where m is the number of accidentyears +## and n is the number of periods to final development. @var{s} may contain u = mn complete years. +## The value @var{s}(i,k), 1<=i<=m, 0<=k<=n1 represents the cumulative losses from accidentperiod 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. +## +## The LD method asumes that exists a development pattern on the individual factors. +## This means that the identity +## @group +## @example +## E[S(i,k) ] +## LDI(k) =  +## E[S(i,k1) ] +## @end example +## @end group +## holds for all k = {0,...,n1} and for all i = {1,...,m}. +## +## @var{quotas} returns a row vector with the cumulative quotas. The transformation +## from individual factors to cumulative quotas is: +## @group +## @example +## l=n1 1 +## @var{quotas}(k) = II  +## l=k+1 LDI(l) +## @end example +## @end group +## +## @seealso {bferguson, ultimateld, quotapanning, quotaad, quotamack} +## @end deftypefn + +## Author: Act. Esteban Cervetto ARG <estebancster@...> +## +## Maintainer: Act. Esteban Cervetto ARG <estebancster@...> +## +## Created: jul2009 +## +## Version: 1.1.0 +## +## Keywords: actuarial reserves insurance bornhuetter ferguson chainladder + +function quotas = quotald(S) + +[m,n] = size (S); #triangle with m years (i=1,2,u,...u+1,u+2,....m) and n periods (k=0,1,2,...n1) +u = m  n; #rows of the upper square +S = fliplr(triu(fliplr(S),u)); #ensure S is triangular + +# calculate the triangle of individual development factors (LDI). +LDI = [ones(m,1), S(:,2:n)./S(:,1:n1)]; +LDI = fliplr(triu(fliplr(LDI),u)); +LDI (m,1) = 0; #last row element without partner + +# weights +W = fliplr(triu(fliplr(S),1u)); #get T values to use +W = shift (W,1,2); #redim k = k1, +W = porcentual(W,1); + +#individual development factors (LDI) or Chainladder factors +LDI_CL = diag(LDI' * W)'; #weighted product +quotas = 1./cumprod(fliplr(LDI_CL)); #calcs cumulated quota +quotas (n) = 1; #last value is 1 +quotas = fliplr(shift(quotas,1)); + +end Added: trunk/octaveforge/main/actuarial/inst/quotamack.m ===================================================================  trunk/octaveforge/main/actuarial/inst/quotamack.m (rev 0) +++ trunk/octaveforge/main/actuarial/inst/quotamack.m 20090725 14:46:47 UTC (rev 6049) @@ 0,0 +1,147 @@ +## Copyright (C) 2009 Esteban Cervetto <estebancster@...> +## +## 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{quotas} =} quotaad (@var{s},@var{v}) +## Calculate the cumulative quotas by the Mack method. +## +## @var{s} is a mxn matrix that contains the runoff triangle, where m is the number of accidentyears +## and n is the number of periods to final development. @var{s} may contain u = mn complete years. +## The value @var{s}(i,k), 1<=i<=m, 0<=k<=n1 represents the cumulative losses from accidentperiod 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 a mx1 vector of known volume measures (like premiums or the number of contracts). +## +## The Mack method asumes that exists a vector @var{v} and a vector P(i) 1<=i<=m of parameters +## such that holds for all i = {1,...,m} the next identity: +## +## @group +## @example +## ultimate(i) = V(i)*P(i) +## @end example +## @end group +## +## where +## +## @group +## @example +## l=n1 +## P(i)= O_mack(i) * E IRL_Mack(l) +## l=0 +## @end example +## @end group +## +## , +## +## @group +## @example +## l=nk1 +## E Z(j,k) +## j=0 +## IRL_Mack(i) =  +## l=nk1 +## E V(i)*O_Mack(l) +## l=0 +## @end example +## @end group +## +## and +## +## @group +## @example +## l=ni1 +## E Z(i,l) +## l=0 +## O_Mack(i) =  +## l=n1 +## E V(i)*IRL(l) (see IRL definition in quotaad function) +## l=0 +## @end example +## @end group +## +## Z represents the incremental losses; then losses satisfy +## Z(k) = (S(k)  S(k1) ),Z(0) = S(0) for all i = {1,...,m}. +## +## @var{quotas} returns a row vector with the cumulative quotas. The formula is: +## @group +## @example +## l=k +## E IRL_Mack(l) +## l=0 +## @var{quotas}(k) =  +## l=n1 +## E IRL_Mack(l) +## l=0 +## @end example +## @end group +## +## @seealso {bferguson, quotald, quotapanning, quotaad} +## @end deftypefn + +## Author: Act. Esteban Cervetto ARG <estebancster@...> +## +## Maintainer: Act. Esteban Cervetto ARG <estebancster@...> +## +## Created: jul2009 +## +## Version: 1.1.0 +## +## Keywords: actuarial reserves insurance bornhuetter ferguson chainladder + +function [quotas] = quotamack (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,...n1) +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:n1)]; +Z = fliplr(triu(fliplr(Z),u)); #clean Z + +# calculate empirical individual loss ratios +a = repmat (V,1,n); +LRI = Z ./ a; + +# weights V(i)/sum(1,nk,V(i)) +num =fliplr(triu(fliplr(a),u)); #numerator and clean low triangle +den = repmat(sum(num),m,1); #denominator +den = fliplr(triu(fliplr(den),u)); #clean low triangle +W = num./den; #divide by +W = fliplr(triu(fliplr(W),u)); + +# incremental Loss Ratios AD +LRI_AD = diag(LRI' * W)'; #weighted product + +if (u==0) +b = (diag(fliplr(S),u) ./ flipud(cumsum(LRI_AD)') ) ./ V; +else +b = ([S(1:u,n); diag(fliplr(S),u)] ./ [sum(LRI_AD)*ones(1,u);flipud(cumsum(LRI_AD)')] ) ./ V; +end + +sZ = sum (Z); #sum of Z +sb = repmat(b,1,n); +sb = fliplr(triu(fliplr(sb),u)); +sV = repmat(V,1,n); +sV = fliplr(triu(fliplr(sV),u)); + +LRI_Mack = sZ ./ (diag(sb'*sV))'; +quotas = cumsum(porcentual(LRI_Mack)); #calculate cumulated quota + +end Added: trunk/octaveforge/main/actuarial/inst/quotapanning.m ===================================================================  trunk/octaveforge/main/actuarial/inst/quotapanning.m (rev 0) +++ trunk/octaveforge/main/actuarial/inst/quotapanning.m 20090725 14:46:47 UTC (rev 6049) @@ 0,0 +1,92 @@ +## Copyright (C) 2009 Esteban Cervetto <estebancster@...> +## +## 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{quotas} =} quotapanning (@var{s}) +## Calculate the cumulative quotas by the Panning method. +## +## @var{s} is a mxn matrix that contains the runoff triangle, where m is the number of accidentyears +## and n is the number of periods to final development. @var{s} may contain u = mn complete years. +## The value @var{s}(i,k), 1<=i<=m, 0<=k<=n1 represents the cumulative losses from accidentperiod 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. +## +## The Panning method asumes that exists a development pattern on the incremental ratios. +## This means that the identity +## @group +## @example +## E[Z(i,k) ] +## B(k) =  +## E[Z(i,0) ] +## @end example +## @end group +## holds for all k = {0,...,n1} and for all i = {1,...,m}. +## Z represents the incremental losses; then losses satisfy +## Z(k) = (S(k)  S(k1) ),Z(0) = S(0) for all i = {1,...,m}. +## +## @var{quotas} returns a row vector with the cumulative quotas. The transformation +## from incremental ratios to cumulative quotas is: +## @group +## @example +## l=k +## E B(l) +# l=0 +## @var{quotas}(k) =  +## l=n1 +## E B(l) +## l=0 +## @end example +## @end group +## +## @seealso {bferguson, ultimatepanning, quotald, quotaad, quotamack} +## @end deftypefn + +## Author: Act. Esteban Cervetto ARG <estebancster@...> +## +## Maintainer: Act. Esteban Cervetto ARG <estebancster@...> +## +## Created: jul2009 +## +## Version: 1.1.0 +## +## Keywords: actuarial reserves insurance bornhuetter ferguson chainladder + +function quotas = quotapanning (S) + +[m,n] = size (S); #triangle with m years (i=1,2,u,...u+1,u+2,....m) and n periods (k=0,1,2,...n1) +u = m  n; #rows of the upper square +S = fliplr(triu(fliplr(S),u)); #ensure S is triangular + +# calculate Z +Z = [S(:,1), S(:,2:n)S(:,1:n1)]; +Z = fliplr(triu(fliplr(Z),u)); #clean Z + +# calc empirical values of the incremental factors +B = Z ./ (Z * [ones(n,1),zeros(n,n1)]'); + +# weights Z(i,0)^2/Z(0)^2 + W = repmat((Z(:,1).^2),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; #divido + W = fliplr(triu(fliplr(W),u)); #clean low triangle + +# Pannings incremental factors +B_Pan = diag(B' * W)'; #weighted product +quotas = cumsum(porcentual(B_Pan)); #cumulated quota + +end Added: trunk/octaveforge/main/actuarial/inst/ultimatead.m ===================================================================  trunk/octaveforge/main/actuarial/inst/ultimatead.m (rev 0) +++ trunk/octaveforge/main/actuarial/inst/ultimatead.m 20090725 14:46:47 UTC (rev 6049) @@ 0,0 +1,66 @@ +## Copyright (C) 2009 Esteban Cervetto <estebancster@...> +## +## 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} =} ultimatead (@var{s},@var{v}) +## Calculate the ultimate values by the Additive method. +## +## @var{s} is a mxn matrix that contains the runoff triangle, where m is the number of accidentyears +## and n is the number of periods to final development. @var{s} may contain u = mn complete years. +## The value @var{s}(i,k), 1<=i<=m, 0<=k<=n1 represents the cumulative losses from accidentperiod 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,...,n1} and for all i = {1,...,m}. +## Z represents the incremental losses; then losses satisfy +## Z(k) = (S(k)  S(k1) ),Z(0) = S(0) for all i = {1,...,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 + +## Author: Act. Esteban Cervetto ARG <estebancster@...> +## +## Maintainer: Act. Esteban Cervetto ARG <estebancster@...> +## +## Created: jul2009 +## +## Version: 1.1.0 +## +## Keywords: actuarial reserves insurance bornhuetter ferguson chainladder + +function [ultimate] = ultimatead (S,V) + +ultimate = ultimatecc(S,V,quotaad(S,V)); + +end Added: trunk/octaveforge/main/actuarial/inst/ultimatecc.m ===================================================================  trunk/octaveforge/main/actuarial/inst/ultimatecc.m (rev 0) +++ trunk/octaveforge/main/actuarial/inst/ultimatecc.m 20090725 14:46:47 UTC (rev 6049) @@ 0,0 +1,106 @@ +## Copyright (C) 2009 Esteban Cervetto <estebancster@...> +## +## 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 runoff triangle, where m is the number of accidentyears +## and n is the number of periods to final development. @var{s} may contain u = mn complete years. +## The value @var{s}(i,k), 1<=i<=m, 0<=k<=n1 represents the cumulative losses from accidentperiod 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,...,n1} 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=n1 +## E S(j,nj) +## j=0 +## @var{quotas}(k) =  +## j=n1 +## E Q(nj)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@...> +## +## Maintainer: Act. Esteban Cervetto ARG <estebancster@...> +## +## Created: jul2009 +## +## 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,...n1) +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 Added: trunk/octaveforge/main/actuarial/inst/ultimateld.m ===================================================================  trunk/octaveforge/main/actuarial/inst/ultimateld.m (rev 0) +++ trunk/octaveforge/main/actuarial/inst/ultimateld.m 20090725 14:46:47 UTC (rev 6049) @@ 0,0 +1,86 @@ +## Copyright (C) 2009 Esteban Cervetto <estebancster@...> +## +## 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} =} ultimateld (@var{s},@var{quotas}) +## Calculate the ultimate values by the Loss Development (Chainladder) method. +## +## @var{s} is a mxn matrix that contains the runoff triangle, where m is the number of accidentyears +## and n is the number of periods to final development. @var{s} may contain u = mn complete years. +## The value @var{s}(i,k), 1<=i<=m, 0<=k<=n1 represents the cumulative losses from accidentperiod 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. +## The 1xn vector @var{quotas} is a set of cumulative quotas calculated by some method. +## +## The LD method asumes that exists a development pattern on the individual factors. +## This means that the identity +## @group +## @example +## E[S(i,k) ] +## LDI(k) =  +## E[S(i,k1) ] +## @end example +## @end group +## holds for all k = {0,...,n1} and for all i = {1,...,m}. +## +## This follows to +## @quotas +## @example +## l=n1 1 +## @var{quotas}(k) = II  +## l=k+1 LDI(l) +## @end example +## @end group +## and the ultimate value is +## @quotas +## @example +## @var{ultimate}(i) = @var{s}(i,ni1) / @var{quotas}(ni1) +## @end example +## @end group +## +## @seealso {bferguson, quotaad, quotapanning} +## @end deftypefn + +## Author: Act. Esteban Cervetto ARG <estebancster@...> +## +## Maintainer: Act. Esteban Cervetto ARG <estebancster@...> +## +## Created: jul2009 +## +## Version: 1.1.0 +## +## Keywords: actuarial reserves insurance bornhuetter ferguson chainladder + +function ultimate = ultimateld (S,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,...n1) +u = m  n; #rows of the upper square +S = fliplr(triu(fliplr(S),u)); #ensure S is triangular + +if (size(quotas) ~= [1,n]) + usage(strcat("quotas must be of size [1,",num2str(n),"]" )); +end + +#calculate the ultimate value + +if (u==0) +ultimate = flipud(diag(fliplr(S))) ./ quotas'; +else +ultimate = [(flipud(diag(fliplr(S),u)) ./ quotas')', S(1:u,n)]'; +end +ultimate = flipud(ultimate); + +end Added: trunk/octaveforge/main/actuarial/inst/ultimatemack.m ===================================================================  trunk/octaveforge/main/actuarial/inst/ultimatemack.m (rev 0) +++ trunk/octaveforge/main/actuarial/inst/ultimatemack.m 20090725 14:46:47 UTC (rev 6049) @@ 0,0 +1,145 @@ +## Copyright (C) 2009 Esteban Cervetto <estebancster@...> +## +## 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} =} ultimatemack (@var{s},@var{v}) +## Calculate the ultimate value by the Mack method. +## +## @var{s} is a mxn matrix that contains the runoff triangle, where m is the number of accidentyears +## and n is the number of periods to final development. @var{s} may contain u = mn complete years. +## The value @var{s}(i,k), 1<=i<=m, 0<=k<=n1 represents the cumulative losses from accidentperiod 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 a mx1 vector of known volume measures (like premiums or the number of contracts). +## +## The Mack method asumes that exists a vector @var{v} and a vector P(i) 1<=i<=m of parameters +## such that holds for all i = {1,...,m} the next identity: +## +## @group +## @example +## ultimate(i) = V(i)*P(i) +## @end example +## @end group +## +## where +## +## @group +## @example +## l=n1 +## P(i)= O_mack(i) * E IRL_Mack(l) +## l=0 +## @end example +## @end group +## +## , +## +## @group +## @example +## l=nk1 +## E Z(j,k) +## j=0 +## IRL_Mack(i) =  +## l=nk1 +## E V(i)*O_Mack(l) +## l=0 +## @end example +## @end group +## +## and +## +## @group +## @example +## l=ni1 +## E Z(i,l) +## l=0 +## O_Mack(i) =  +## l=n1 +## E V(i)*IRL(l) (see IRL definition in quotaad function) +## l=0 +## @end example +## @end group +## +## Z represents the incremental losses; then losses satisfy +## Z(k) = (S(k)  S(k1) ),Z(0) = S(0) for all i = {1,...,m}. +## +## @var{ultimate} returns a column vector with the m ultimate values. Following the main equation: +## @group +## @example +## @var{ultimate}(i) = V(i)*P(i) +## @end example +## @end group +## +## @seealso {bferguson, quotald, quotapanning, quotaad, quotamack} +## @end deftypefn + +## Author: Act. Esteban Cervetto ARG <estebancster@...> +## +## Maintainer: Act. Esteban Cervetto ARG <estebancster@...> +## +## Created: jul2009 +## +## Version: 1.1.0 +## +## Keywords: actuarial reserves insurance bornhuetter ferguson chainladder + + +function ultimate = ultimatemack (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,...n1) +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 + +# calcs Z triangle +Z = [S(:,1), S(:,2:n)S(:,1:n1)]; +Z = fliplr(triu(fliplr(Z),u)); #clean Z + +# calculate empirical individual loss ratios +a = repmat (V,1,n); +LRI = Z ./ a; + +# weights V(i)/sum(1,nk,V(i)); +num =fliplr(triu(fliplr(a),u)); #numerator, and clean low triangle +den = repmat(sum(num),m,1); #denominator +den = fliplr(triu(fliplr(den),u)); #clean low triangle +W = num./den; #divide +W = fliplr(triu(fliplr(W),u)); + +# incremental Loss Ratios AD +LRI_AD = diag(LRI' * W)'; #weighted product + +if (u==0) +b = (diag(fliplr(S),u) ./ flipud(cumsum(LRI_AD)') ) ./ V; +else +b = ([S(1:u,n); diag(fliplr(S),u)] ./ [sum(LRI_AD)*ones(1,u);flipud(cumsum(LRI_AD)')] ) ./ V; +end + +sZ = sum (Z); # sum of Z +sb = repmat(b,1,n); +sb = fliplr(triu(fliplr(sb),u)); +sV = repmat(V,1,n); +sV =fliplr(triu(fliplr(sV),u)); + +LRI_Mack = sZ ./ (diag(sb'*sV))'; + +K_Mack = b * sum(LRI_Mack); + +ultimate = K_Mack .* V; + +end Added: trunk/octaveforge/main/actuarial/inst/ultimatepanning.m ===================================================================  trunk/octaveforge/main/actuarial/inst/ultimatepanning.m (rev 0) +++ trunk/octaveforge/main/actuarial/inst/ultimatepanning.m 20090725 14:46:47 UTC (rev 6049) @@ 0,0 +1,73 @@ +## Copyright (C) 2009 Esteban Cervetto <estebancster@...> +## +## 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} =} ultimatepanning (@var{s},@var{quotas}) +## Calculate the ultimate value by the Panning method. +## +## @var{s} is a mxn matrix that contains the runoff triangle, where m is the number of accidentyears +## and n is the number of periods to final development. @var{s} may contain u = mn complete years. +## The value @var{s}(i,k), 1<=i<=m, 0<=k<=n1 represents the cumulative losses from accidentperiod 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. +## The 1xn vector @var{quotas} is a set of cumulative quotas calculated by some method. +## +## The Panning method asumes that exists a development pattern on the incremental ratios. +## This means that the identity +## @group +## @example +## E[Z(i,k) ] +## B(k) =  +## E[Z(i,0) ] +## @end example +## @end group +## holds for all k = {0,...,n1} and for all i = {1,...,m}. +## Z represents the incremental losses; then losses satisfy +## Z(k) = (S(k)  S(k1) ),Z(0) = S(0) for all i = {1,...,m}. +## +## @var{ultimate} returns a column vector with the ultimate values. Their values are: +## @group +## @example +## @var{ultimate}(i) = Z(i,0)*quotas(0) +## @end example +## @end group +## +## @seealso {bferguson, quotapanning, quotald, quotaad} +## @end deftypefn + +## Author: Act. Esteban Cervetto ARG <estebancster@...> +## +## Maintainer: Act. Esteban Cervetto ARG <estebancster@...> +## +## Created: jul2009 +## +## Version: 1.1.0 +## +## Keywords: actuarial reserves insurance bornhuetter ferguson chainladder + +function [ultimate] = ultimatepanning (S,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,...n1) +u = m  n; #rows of the upper square +S = fliplr(triu(fliplr(S),u)); #ensure S is triangular + +if (size(quotas) ~= [1,n]) + usage(strcat("quotas must be of size [1,",num2str(n),"]" )); +end + +ultimate = S(:,1) / quotas(1); + +end This was sent by the SourceForge.net collaborative development platform, the world's largest Open Source development site. 
From: <paramaniac@us...>  20090725 09:38:35

Revision: 6048 http://octave.svn.sourceforge.net/octave/?rev=6048&view=rev Author: paramaniac Date: 20090725 09:38:23 +0000 (Sat, 25 Jul 2009) Log Message:  margin: ensured that frequencies are real Modified Paths:  trunk/octaveforge/main/control/inst/margin.m Modified: trunk/octaveforge/main/control/inst/margin.m ===================================================================  trunk/octaveforge/main/control/inst/margin.m 20090724 20:12:27 UTC (rev 6047) +++ trunk/octaveforge/main/control/inst/margin.m 20090725 09:38:23 UTC (rev 6048) @@ 126,7 +126,7 @@ if (length (idx) > 0) # if frequencies in R+ exist  w_gm = w(idx); + w_gm = real (w(idx)); for k = 1 : length (w_gm) f_resp(k) = polyval (num_jw, w_gm(k)) / polyval (den_jw, w_gm(k)); @@ 199,7 +199,7 @@ if (length (idx) > 0) # if frequencies in R+ exist  w_pm = w(idx); + w_pm = real (w(idx)); for k = 1 : length (w_pm) f_resp = polyval (num_jw, w_pm(k)) / polyval (den_jw, w_pm(k)); This was sent by the SourceForge.net collaborative development platform, the world's largest Open Source development site. 