随机过程matlab程序

0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-6
-4
-2
0
2
4
6
44798133900177/281474976710656 exp(-5/2 x 2+3 x y-y 2 )
0.2
0.15
0.1
0.05
0
5 0
5 0
y
-5
-5
x
% % The daily log returns on the stock have a mean of 0.05/year and a standard deviation of 0.23/year. These can be converted to rates per trading day by deviding by 253 and sqrt(253), respectively.
% A=normrnd(mu,sigma,1,N)
capmu=mean(x)
tao=1 x1=A.*cos(w*(t+tao)+theta); capgamma=mean((x-capmu).*(x1-capmu))
% m time simulation clear; w=2; N=1000; mu=2; sigma=3; m=500;capmu1=[];capgamma1=[]; for i=1:m
rho=(1+s*t)/(sigma1*sigma2); f=1/(2*pi*sigma1*sigma2*sqrt(1-rho^2))*exp(-1/(2*(1-rho^2))*((x-mu1)^2/sigma1^ 2-2*rho*(x-mu1)*(y-mu2)/(sigma1*sigma2)+(y-mu2)^2/sigma2^2)); ezsurf(f)
capmu=mean(capmu1); capgamma=mean(capgamma1);
err1=mean((capmu1-0).^2); gamma=(sigma^2+mu^2)*cos(w*tao)/2; err2=mean((capgamma1-gamma).^2); [capmu,capgamma; err1, err2]
% 输出： 0.0058 -2.7005 0..5 -2
-2.5 -3
-3.5 -4 0
50 100 150 200 250 300 350 400 450 500
Question 1: What is the probability that the value of the stock will be below $950,000 at the close day of at least one of the next 45 trading days?
clear; niter=1.0E5; below=repmat(0,1,niter); randn( 'seed' ,0); for i=1:niter
% generate random numbers % minmum price over next 45 days
% P29 随机相位正弦波仿真 % 1 time simulation w=2; N=1000; mu=2; sigma=3; s=rand('state'); A=mu+sigma*randn(1,N); theta=-pi+2*pi*rand(1,N); t=1:N; x=A.*cos(w*t+theta);
% PPT 例 2 一维正态密度与二维正态密度 syms x y; s=1; t=2; mu1=0; mu2=0; sigma1=sqrt((1+s^2)); sigma2=sqrt((1+t^2));
x=-6:0.1:6; f1=1/sqrt(2*pi*sigma1)*exp(-(x-mu1).^2/(2*sigma1^2)); f2=1/sqrt(2*pi*sigma2)*exp(-(x-mu2).^2/(2*sigma2^2)); plot(x,f1,'r-',x,f2,'k-.')
s=rand('state'); A=mu+sigma*randn(1,N); theta=-pi+2*pi*rand(1,N); t=1:N; x=A.*cos(w*t+theta); capmu=mean(x); capmu1=[capmu1,capmu];
tao=1; x1=A.*cos(w*(t+tao)+theta); capgamma=mean((x-capmu).*(x1-capmu)); capgamma1=[capgamma1,capgamma]; end plot(1:m,capmu1,'*',1:m,capgamma1,'o')
r=normrnd(0.05/253,0.23/sqrt(253),1,45); logPrice=log(1.0E6)+cumsum(r); minlogP=min(logPrice); below(i)=sum(minlogP<log(950000)); end Pro=mean(below)
% number of iterations % set up storage