nested quadrature in matlab using two quadrature rules - matlab

Question

Stuck on numerically evaluating this integral and only have experience in doing simple quadrature schemes so bear with me if this looks amateurish. The nested integral is below using Gauss-Hermite(-inf,+inf) and a variant of Gauss Laguerre scheme (0,+inf) - over a gaussian and gamma(v/2,2) densities. I get to the point where the I m nearly finished the integration, intermediate steps look good, but I m stuck on how to combine the weights to evaluate the overall integral. I'd be really grateful for suggestions in modifing the code/other idea to code a better quadrature scheme that solves the problem.
\begin{equation}
\int^{\infty}{-\infty}\int^{\infty}{0} \prod_{i=1}^n\Phi \left(\frac{\sqrt{w/v}\,C{i}-a{i}Z}{\sqrt{1a {i^2}}\right)f{z}(Z)f{w}(W)dwdz
\end{equation}
% script defines nodes, weights, parameters then calls one main and one subfunction
rho=0.3; nfirms=10; h=repmat(0.1,[1,nfirms]); T=1; R=0.4; v=8; alpha=v/2;GaussPts=15;
% Quadrature nodes - gaussian and gamma(v/2) from Miranda and Fackler CompEcon
% toolbox
[x_norm,w_norm] = qnwnorm(GaussPts,0,1);
[x_gamma,w_gamma] = qnwgamma(GaussPts,alpha);
L_mat=zeros(nfirms+1,GaussPts);
for i=1:1:GaussPts;
L_mat(:,i) = TC_gamma(x_norm(i,:),x_gamma(i,:),h,rho,T,v,nfirms);
end;
w_norm_mat= repmat(w_norm',nfirms+1,1);
w_gamma_mat = repmat(w_gamma',nfirms+1,1);
% need to weight L_mat by the gaussian and chi-sq i.e, (gamma v/2,2)?
ucl = L_mat.*w_norm;%?? HERE
ucl2 = sum(ucl.*w_gamma2,2);% ?? HERE
function [out] = TC_gamma(x_norm,x_gamma,h,rho,T,v,nfirms)
% calls subfunction feeds into recursion
qki= Vec_CondPTC_gamma(x_norm,x_gamma,h,rho,T,v)' ;
fpdf=zeros(nfirms+1,nfirms+1);
% start at the first point on the tree
fpdf(1,1)=1;
for i=2:nfirms+1 ;
fpdf(1,i)=fpdf(1,i-1)*(1-qki(:,i-1));
for j=2:nfirms+1;
fpdf(j,i)=fpdf(j,i-1)*(1-qki(:,i-1))+fpdf(j-1,i-1)*qki(:,i-1);
end
fpdf(i,i)=fpdf(i-1,i-1)*qki(:,i-1);
end
out=fpdf(:,end);
end% of function TC_gamma
function qki= Vec_CondPTC_gamma(x_norm,x_gamma,h,rho,T,v)
PD = (1-exp(-kron(h,T)));DB = tinv(PD,v);
a=rho.^0.5; sqrt1_a2 = sqrt(1-sum(a.*a,2));
aM = gtimes(a, x_norm'); Sqrt_W=gamcdf(x_gamma,v/2,2).^0.5;
DB_times_W= gtimes(DB,Sqrt_W); DB_minus_aM = gminus(DB_times_W',aM);
qki=normcdf(grdivide(DB_minus_aM,sqrt1_a2));
end% of function Vec_CondPTC