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| %Initial param
yield;
randn('state',24)
theta=0.37;
sigma_r=0.01;
sigma_s=0.6;
sigma_l=0.4;
sigma_e=0.21;
lambda_s=0.06;
lambda_l=0.05;
lambda_e=0.12;
rho=0.001;
T=5;
dt= 1/250;
t=1:dt:T;
N=length(t);
%Calcul pi_s and pi_l
B=zeros(1,N);
gamma= 0.5;
B =(gamma/theta).*(exp(theta*(T-t))-1);
k =(1-exp(-theta*(T-t)))/theta;
pi_s= 1/(1-gamma)*(lambda_s/sigma_s)-(gamma/(1-gamma))* sigma_r/sigma_l .*k;
pi_l= 1/(1-gamma)*(lambda_l/sigma_l)-(gamma/(1-gamma))* sigma_r/sigma_l .*k;
pi_b= 1-pi_s-pi_l;
%calcul capital adequacy
x = pi_s(1:end-864);
y = pi_l(1:end-864);
alpha1= r' + (x + y).*lambda_e;
alpha2=(x+y).*sigma_e;
alpha3=rho;
beta1=0.2.*x*(r+lambda_s)+0.5.*y*(r+lambda_l)-(0.2.*x*sigma_s).^2-(0.5.*y*sigma_l).^2;
beta2=0.5.*y*sigma_l;
beta3=0.2.*x*sigma_s;
xzero=0.92;
T=5;
N=2^7;
dt=T/N;
dw1=sqrt(dt)*randn(1,N);
dw2=sqrt(dt)*randn(1,N);
dw3=sqrt(dt)*randn(1,N);
%Simulation
R=4; dt=R*dt; L=N/R;
xtemp=zeros(1,L);
xtemp=xzero;
for j=1:L
winc1=sum(dw1(R*(j-1)+1:R*j));
winc2=sum(dw2(R*(j-1)+1:R*j));
winc3=sum(dw3(R*(j-1)+1:R*j));
xtemp=xtemp + (xtemp.*(alpha1 - beta1)- alpha3)*dt - xtemp.*(beta2*winc1 + beta3*winc2 - alpha2*winc3);
xem(j)=xtemp';
end
plot([0:dt:T],[xzero,xem],'k')
y=0.8;
hold on
hline=refline([0 y]);
set (hline, 'color', 'r')
xlabel('time','Fontsize',12)
ylabel('k(t)', 'Fontsize', 16)
title('Simulation de la dynamique CAR') |
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