ma=1; t = 0; it = 1; hs=1/nn;

px=project2 4; x=xm(:,1);

jm=nqq(px,nx,nu,nn,zz,ma,t,it,hs,sm,x,lm,ns);

f=jm(nn+1);

g(1)=sum(sm)-1;

%Project2 3.m compute differential equation

function ff = project2 3(t,it,z,yin,hs,sm,xm,lm,ns)

nn=1/hs;

T=5;

B=0.0;

B=0.1;

B=0.2;

nb=nn/ns;

rr=nn/(2*ns);

%for i=1:rr,

% ut(2*i-1)=2;

% ut(2*i)=-2;

%end

for i=1:rr,

ut(2*i-1)=2; ut(2*i)=-2;

ts=zeros(nn,1); if ns > 1 for ii= 1:nb

for jj=1:ns

ts(ii)=ts(ii)+sm((ii-1)*ns+jj);

end else

for ii= 1: nb

ts(ii)=sm(ii);

pt=nb*ts((floor((it-1)/ns)+1),1); %ff(1) = T*z(2)*nn*sm(1,floor(it));

%ff(2) = (-T*z(1)+T*ut(1,floor((it-1)/ns)+1)-T2*B*z(2)) *nn*sm(1,floor(it));

ff(1)= T * z(2)*pt;

ff(2)= (-T * z(1) + T *ut(1,(floor((it-1)/ns)+1)) -Тл2 * В *z(2))*pt;

%ff=ut(1,(floor((it-1)/ns) + 1))*nn*sm(1,floor(it)); %ff=ut(1,(floor((it-1)/ns) +1))*pt;

%project2 4.m

function ff = project2 4(t,it,z,yin,hs,sm,x,lm,ns)

nn=1/hs;

fr=nn*mod(t,hs);

xmt=(1-fr)*x(it)+fr*x(it+1);

nb=nn/ns;

umx=zeros(nn,1);

umx(2)=sm(1);

for ii = 3: nn

umx(ii)=sm(ii-1)+umx(ii-1);

qt=nn*s(floor(it),1)*(t-hs*(it-1))+umx(floor(it),1);

%qt=nb*ts((floor((it-1)/ns) +1),1)*(t-hs*ns*((

floo:r((it-l)/rs;)+l)-l)) ;

%qt=qt+umx((floor((it-1)/ns)+1) ,1);

ll=abs (xmt-((-5)*qt+5));% x1(t)-((-5*t)+5)

*ll= (xrrt-((-5)*qt+5))A2;

%ll=abs (xmt-0.4*(qt2));

%ll=(xmt-qt)*2;

ff=ll*nn*sm(floor(it),1);

%ff=ll*pt;

%Project2 4 test.m

function ff = project2 4 test(t,it,z,yin,hs,sm,x,lm,ps)

nn=1/hs;

fr=nn*mod(t,hs);

xmt=(1-fr)*x(it)+fr*x(it+1);

umx=zeros(nn,1);

umx(2) = sm(1);

for ii=3:nn

umx(ii)=umx(ii-1) + sm(ii-1);

u=zeros(nn/ps,1); ts=zeros(nn/ps,1);

if ps > 1

for ii= 1:nn/ps

u(ii*ps-(ps-1))=sm(ii*ps-(ps-1));

for jj=ii*ps-(ps-2):ii*ps

u(jj)=u(jj-1)+sm(jj);

ts(ii)=u(jj);

end else

for ii = 1: nn/ps

ts(ii)=sm(ii)

pt=(nn/ps)*ts((floor((it-1)/ps)+1),1); qt=nn*sm(1,floor(it))*(t-hs*(it-1))+umx(floor(it),1); %ll=abs (xmt-((-5)*qt+5));% x1(t)-((-5*t)+5) ll=(xmt-((-5)*qt+5))A2; ff=im*ll*sm(1,floor(it))*pt;

3. Program C: Optimal Financing Model in Chapter 4

% An application of a model of investment of an utility. %Model1 1.m

function model1 1=model1 1(nb,ns,parameters) % parameters

here is used to define all the parameters in the model

%parameters = [p k r d c T]; % parameters here is used

to define all the parameters in the model

%parameters=[ 0.1 0.15 0.2 0.1 1 1];

par = [2,2,nb,ns,parameters];

%xinit= [P0,E0];

%xinit=[1 1];

%xinit = [0.5,0.5];

%xinit=[1.5 1.5];

xinit=[3 2];

nb=par(3); % big intervals

ns=par(4); % small intervals

nn=nb*ns; %total intervals

options(13)=1;

options(14)=10000;

um0=ones(nb,1)/nb;

%um=[0.1,0.3,0.6];

ul=zeros(nb,1); uu=ones(nb,1);

um=constr(model1 2,um0,options,ul.uu,[],xinit,par); [f,g,xm] = model1 2(um,xinit,par) sm=zeros(nn,1); v=zeros(nn,1);

for ii =1: nb

for jj= 1:ns

sm((ii-1)*ns+jj)=um(ii)/ns;

v(1)=sm(1);

for ii=2:nn

v(ii)=sm(ii)+v(ii-1);