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141 lines
2.9 KiB
141 lines
2.9 KiB
%投资利益与风险1998A题
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%模型一 给定风险承受程度，求最大利益
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f=[-0.05,-0.27,-0.19,-0.185,-0.185];
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%A矩阵
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%A=[0,0.025,0.015,0.055,0.026]; %错误
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%b=[1,1,1,1,1];
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A=[zeros(4,1),diag([0.025,0.015,0.055,0.026])];%不等式约束条件矩阵
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%Aeq、beq
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Aeq=[1,1.01,1.02,1.045,1.065];
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beq=1;
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%lb
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%lb=0; %错误
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lb=zeros(5,1);
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%可承担风险率a
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a=(0:0.001:0.05);
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%保存最优解
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Q=zeros(1,length(a));
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xx=[];%空矩阵存放最优解对应x的值
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for i=1:length(a)
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b=a(i)*ones(4,1);
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[x,y]=linprog(f,A,b,Aeq,beq,lb);
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Q(i)=-y;%注意取负！！！
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xx=[xx;x'];
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end
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plot(a,Q,'*r');
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xlabel("风险率");
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ylabel("最大收益");
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%模型二 收益、风险按权重组合
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% f0=[-0.05,-0.27,-0.19,-0.185,-0.185];
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% w=(0:0.1:1);
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% Aeq=[1,1.01,1.02,1.045,1.065,0];
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% beq=1;
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% lb=0;
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% xx=[];
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% Q=zeros(1,length(w));
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% A=[zeros(5,1),diag([0.025,0.025,0.055,0.065,0])];
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% b=ones(5,1);
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% for i=1:length(w)
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% f=[-w(i)*f0,1-w(i)];
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% b=x(end)*b;
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% [x,y]=linprog(f,A,b,Aeq,beq,lb);
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% Q(i)=-y;
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% xx=[xx,x'];
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% end
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% plot(w,Q,'*r');
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%模型二 收益、风险按权重组合
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clc; clear; close all; format long g;
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M = 10000;
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prob = optimproblem;
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x = optimvar('x', 6, 1, 'LowerBound', 0);
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r = [0.05, 0.28, 0.21, 0.23, 0.25];
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p = [0, 0.01, 0.02, 0.045, 0.065];
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q = [0, 0.025, 0.015, 0.055, 0.026]';
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%w = 0:0.1:1;
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w = 0.7:0.03:1;
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V = [];
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Q = [];
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X = [];
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prob.Constraints.con1 = (1 + p) * x(1:end-1) == M;
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prob.Constraints.con2 = (q(2:end).* x(2:end-1))<= x(end); %下标从1开始
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for i = 1:length(w)
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prob.Objective = w(i) * x(end) - (1 - w(i)) * (r - p) * x(1:end-1); %注意大小写
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[sol, fval, flag, out] = solve(prob);
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xx = sol.x;
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V = [V, max(q.* xx(1:end-1))];
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Q = [Q, (r - p) * xx(1:end-1)];
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X = [X, xx];
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plot(V, Q, '*-');
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grid on;
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xlabel('风险');
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ylabel('收益');
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end
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%模型三：达到一定盈利水平，极小化风险
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clc; clear; close all; format long g;
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M=10000;
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k=1500:100:3000;
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prob = optimproblem;
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x = optimvar('x', 5, 1, 'LowerBound', 0);%下界为0
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r = [0.05, 0.28, 0.21, 0.23, 0.25];
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p = [0, 0.01, 0.02, 0.045, 0.065];
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q = [0, 0.025, 0.015, 0.055, 0.026]';
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V = [];
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Q = [];
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X = [];
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t = optimvar('t', 'LowerBound', 0);
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%prob.Objective=max(q.*x);%极小化风险
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for i=1:length(k)
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prob.Objective = t; % 极小化风险
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prob.Constraints.con1 = (1 + p) * x == M;
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prob.Constraints.con2=((r-p)*x>=k(i));%达到一定盈利水平
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prob.Constraints.con3=(q.*x<=t);
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[sol,fval,flag,out]=solve(prob);
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if flag==1
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xx=sol.x;
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X=[X,xx];
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Q=[Q,(r-p)*xx];
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V=[V,fval];
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else
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xx=-1*ones(5,1);
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X=[X,xx];
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Q=[Q,-1];
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V=[V,-1];
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end
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end
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plot(k,V,'*-');
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