金融工学と最適化

#金融工学と最適化　p.41

library(dplyr)

R_bar=c(14,8,20);sigma=c(6,3,15)

p=matrix(c(1,0.5,0.2,0.5,1,0.4,0.2,0.4,1),ncol=3)

R_f=5

cov=t(t(sigma))%*%t(sigma)*p

Z=solve(cov)%*%c(R_bar-R_f)

X=Z/sum(Z)

R_p=t(X)%*%t(t(R_bar))

sigma_p=(t(X)%*%cov)%*%X

C=solve(cov)

C0=C%*%R_bar

C1=-C%*%rep(R_f,length(R_bar))

#p.68


R_bar=c(14,8,20);sigma=c(6,3,15)

p=matrix(c(1,0.5,0.2,0.5,1,0.4,0.2,0.4,1),ncol=3)

cov=t(t(sigma))%*%t(sigma)*p;C=solve(cov)

D1=C%*%rep(1,nrow(C));D2=C%*%R_bar;r_E=10

a11=sum(D1);a12=sum(D2);a22=sum(D2*R_bar)

mat=matrix(c(a11,a12,a12,a22),ncol=2)

lambda=solve(mat/2,c(1,r_E))

X=(lambda[1]/2)*C%*%rep(1,nrow(C))+(lambda[2]/2)*C%*%R_bar

#p.79

R_it=c(10,3,15,9,3);R_mt=c(4,2,8,6,0)

beta=sum((R_it-mean(R_it))*(R_mt-mean(R_mt)))/sum((R_mt-mean(R_mt))^2)

alpha=mean(R_it)-beta*mean(R_mt)

sigma_ei=sum((R_it-alpha-beta*R_mt)^2)/length(R_it)

R2=cor(R_it,R_mt)^2

#数理計画入門　p.26

B=t(matrix(c(3,2,1,2),ncol=2));N=t(matrix(c(2,1,2,0),ncol=2))

b=c(12,8);c=c(-1,-1)

x_b=solve(B)%*%b

B%*%x_b

#p.51　内点法

C=-sample(1:60,18,replace=T)

A=matrix(sample(1:60,prod(length(C)^2),replace=T),ncol=length(C))

B=sample(1:60,length(C),replace=T)

s=rep(100,length(C));w=rep(100,length(C));x=rep(100,length(C))


ite=10000;

alpha=0.0001

for(j in 1:ite){

mu=sum(x*s)/(length(C)^2)  

if(mu>10^(-5)){  

x_pre=x;w_pre=w;s_pre=s;  

s_mat=diag(s);x_mat=diag(x);e=rep(1,length(C)) 

p=rep(mu,length(C))-(x_mat%*%s_mat%*%e)

q=B-c(A%*%x);

r=C-c(t(A)%*%w)-s

delta_w=solve(A%*%solve(s_mat)%*%x_mat%*%t(A),q-A%*%solve(s_mat)%*%(p-x_mat%*%r))

delta_s=r-t(A)%*%delta_w

delta_x=solve(s_mat)%*%(p-x_mat%*%delta_s) 

if(sum(x+alpha*c(delta_x)>0)==length(x) & sum(s+alpha*c(delta_s)>0)==length(s)){

x=x+alpha*c(delta_x);w=w+alpha*c(delta_w);s=s+alpha*c(delta_s)

print(sum(abs(x-x_pre)+abs(w-w_pre)+abs(s-s_pre)))

}else{

print("stop")  

}

}else{

print("stop")  


}


}