% PLOTAPDES.M   
%   PLOTAPDES.M plots the 2D-graphs corresponding to the expected shortfall
%   of an APD r.v. with parameters alpha and lda. 
%
% Comments: 
%   a standard alpha-quantile r.v. X has pdf :
%   p(alpha,lda,x) = [A^(1/lda)/gamma(1+1/lda)]*...
%                   *exp[-(A/alpha^lda)*abs(x)^lda],        if x <= 0,
%                   *exp[-(A/(1-alpha)^lda)*abs(x)^lda],    if x > 0,
%   where A = (2*alpha^lda*(1-alpha)^lda)/(alpha^lda+(1-alpha)^lda).
%
% References:
%   [1] Komunjer, I. (2006): "Asymmetric Power Distribution: Theory and 
%   Applications to Risk Measurement"
%
% Author: Ivana Komunjer - UCSD (komunjer@ucsd.edu)
% Version: 2.1        Date: 06/07/2006

% Inputs the values of alpha and lda
pp = (0.005:0.005:0.995)';
aa1 = 0.1*ones(199,1);
aa2 = 0.2*ones(199,1);
aa3 = 0.3*ones(199,1);
aa5 = 0.5*ones(199,1);
ll7 = 0.7*ones(199,1);
ll1 = 1*ones(199,1);
ll2 = 2*ones(199,1);
ll4 = 4*ones(199,1);
% ES with lda = 0.7
y71 = AlphaQuantES(pp,aa1,ll7);
y72 = AlphaQuantES(pp,aa2,ll7);
y73 = AlphaQuantES(pp,aa3,ll7);
y75 = AlphaQuantES(pp,aa5,ll7);
% ES with lda = 1
y11 = AlphaQuantES(pp,aa1,ll1);
y12 = AlphaQuantES(pp,aa2,ll1);
y13 = AlphaQuantES(pp,aa3,ll1);
y15 = AlphaQuantES(pp,aa5,ll1);
% ES with lda = 2
y21 = AlphaQuantES(pp,aa1,ll2);
y22 = AlphaQuantES(pp,aa2,ll2);
y23 = AlphaQuantES(pp,aa3,ll2);
y25 = AlphaQuantES(pp,aa5,ll2);
% ES with lda = 4
y41 = AlphaQuantES(pp,aa1,ll4);
y42 = AlphaQuantES(pp,aa2,ll4);
y43 = AlphaQuantES(pp,aa3,ll4);
y45 = AlphaQuantES(pp,aa5,ll4);
% Generates first graph
subplot(2,2,1)
plot(pp,y41,'b:',pp,y21,'g-',pp,y11,'m-.',pp,y71,'r--');
axis([0 1 0 5])
title('Alpha = .1');
subplot(2,2,2)
plot(pp,y42,'b:',pp,y22,'g-',pp,y12,'m-.',pp,y72,'r--');
axis([0 1 0 5])
title('Alpha = .2');
subplot(2,2,3)
plot(pp,y43,'b:',pp,y23,'g-',pp,y13,'m-.',pp,y73,'r--');
axis([0 1 0 5])
title('Alpha = .3');
subplot(2,2,4)
plot(pp,y45,'b:',pp,y25,'g-',pp,y15,'m-.',pp,y75,'r--');
axis([0 1 0 5])
title('Alpha = .5');
legend('lambda = 4','lambda = 2', 'lambda = 1', 'lambda = .7');

% Generates second graph
subplot(2,2,1)
plot(pp,y41,'b:',pp,y21,'g-',pp,y11,'m-.',pp,y71,'r--');
axis([0 1 0 5])
title('Alpha = .1');
subplot(2,2,2)
plot(pp,y42,'b:',pp,y22,'g-',pp,y12,'m-.',pp,y72,'r--');
axis([0 1 0 5])
title('Alpha = .2');
subplot(2,2,3)
plot(pp,y43,'b:',pp,y23,'g-',pp,y13,'m-.',pp,y73,'r--');
axis([0 1 0 5])
title('Alpha = .3');
subplot(2,2,4)
plot(pp,y45,'b:',pp,y25,'g-',pp,y15,'m-.',pp,y75,'r--');
axis([0 1 0 5])
title('Alpha = .5');
legend('lambda = 4','lambda = 2', 'lambda = 1', 'lambda = .7');
subplot(2,2,1)
plot(pp,y71,'b:',pp,y72,'g-',pp,y73,'m-.',pp,y75,'r--');
axis([0 1 0 5])
title('Lambda = .7');
subplot(2,2,2)
plot(pp,y11,'b:',pp,y12,'g-',pp,y13,'m-.',pp,y15,'r--');
axis([0 1 0 5])
title('Lambda = 1');
subplot(2,2,3)
plot(pp,y21,'b:',pp,y22,'g-',pp,y23,'m-.',pp,y25,'r--');
title('Lambda = 2');
subplot(2,2,4)
plot(pp,y41,'b:',pp,y42,'g-',pp,y43,'m-.',pp,y45,'r--');
axis([0 1 0 5])
title('Lambda = 4');
legend('alpha = .1','alpha = .2', 'alpha = .3', 'alpha = .5');