I have been badly stuck up with the following code.
if true n=35; T=15; g=.111;K=1/g;d=2; rbar=0.04;mubar=0; R=[1, 0; 0, 0];M=[0, 0; 0, 1];X012=0.002;X0=[0.01, X012; X012, 0.001];H=[-0.5, 0.4; 0.007, -0.008];Q=[0.06 -0.0006; -0.06, 0.006];Scheck7=0;beta=3;SIGMA=[0.006811791307233, -0.000407806990090; -0.000407806990090, 0.00039291243623];PSICURL=[0.011526035149236, 0.758273970303934; 0.013935191202735, 0.955423605940771]; %Specifications of the arrays for the Levy Assumption
S0i=zeros(n,1);S0i2=zeros(n,1);Yn0=0; %Used in the first lower bound
Yi=zeros(n,1);%Arrays for the MC estimate
S1MC=zeros(n,1);POW=zeros(n,1);SPOW=0;SPHI=0;SPSI=0;% Parameters used for the new approach
% To define the Matrices PSIi in an array
delta=0.75; %The damping factor
PSIi = cell(1, n);PHIi=zeros(n,1);% Prameters for the symbolic sum
% Remember our x is Gamma1
%syms x ik
% Computation of Rho
Num=(Q(1,1)*Q(1,2)+Q(2,2)*Q(2,1))*X0(1,2);Denom=sqrt((Q(1,1)^2+Q(2,1)^2)*X0(1,1)*(Q(2,2)^2+Q(1,2)^2)*X0(2,2));Rho=Num/Denom% Specification of new MATRICES Aij's
ANEW=expm([T.*H,T.*(2*(Q'*Q));T.*(R+M),T.*(-(H'))]);A11=ANEW(1:2,1:2); %That is good
A21=ANEW(3:4,1:2);A12=ANEW(1:2,3:4);%intersection
A22=ANEW(3:4,3:4);% Computationof psi(T) and phi(T) (Otherwise with varying i;run in a loop)
C22=inv(A22);PSIT=C22*A21;PHIT=beta*(log(det(A22))+T*trace(H'))/2;% Computation of SZCB's Pcurl(0,T)
C=trace(PSIT*X0);SZCB=exp(-(rbar+mubar)*T)*exp(-PHIT-C)SIGMAi=inv(SIGMA);THETA1=SIGMAi*(PSICURL'*X0*PSICURL);for i=2:n; APHNEW=expm([(i-1).*H,(i-1).*(2*(Q'*Q));(i-1).*(R+M),(i-1).*(-(H'))]); APHNEW11=APHNEW(1:2,1:2); %That is good APHNEW21=APHNEW(3:4,1:2); APHNEW12=APHNEW(1:2,3:4); APHNEW22=APHNEW(3:4,3:4); % Computation of PSIi and PHIi
BPHNEW22=inv(APHNEW22); PSIi{i}=APHNEW22\APHNEW21; M7=PSIi{i}; SPSI=SPSI+PSIi{i}; PHIi(i)=beta*(log(det(APHNEW22))+(i-1)*trace(H'))/2; S0i(i)=exp(-((rbar+mubar)*(i-1)+PHIi(i))); S0i2(i)=(-((rbar+mubar)*(i-1)+PHIi(i))); Yn0=Yn0+S0i2(i);endSIGMAi=inv(SIGMA);THETA1=SIGMAi*(PSICURL'*X0*PSICURL);fun4 = @(Gamma1) exp(-(1i.*Gamma1).*log(K-1)).*exp((1i.*Gamma1+(delta+1)).*Yn0).*(exp(trace(1i.*(THETA1*inv(eye(2)-2i.*SIGMA*((-(Gamma1-1i.*(delta+1))).*SPSI))*SIGMA*((-(Gamma1-1i.*(delta+1))).*SPSI))))./((det(eye(2)-2i.*SIGMA*((-(Gamma1-1i.*(delta+1))).*SPSI))).^(beta./2)))./(delta.^2+delta-Gamma1.^2+(1i.*Gamma1.*(2.*delta+1)));qty = quadgk(fun4,0,inf)qty1= exp(-(delta*log(K-1)))*qty/piLB1=g*SZCB*qty1format 'long'end
The numerical integration involves matrices. I am unable to use quadgk. Can anyone please help?
Thanks in advance.
Best Answer