why do I receive an error in my codes?

I am trying to find the maximum of the function.I want to find teta for each x which is maximize the my function. the function is

   F(x)=(F(x-1)+cr*Y(x-1))*exp(r+teta(x-1)*((mu-1/2*sigma.^2)+sigma*Z(1,x)))

I write the codes but it has errors. could you possibly help me?

lambda=4.5;  % loss aversion ratio
nu1=0.44;    % curvature parameter for gains
nu2=0.88;    % curvature parameter for loss
rl=0.02;
sigma1=0.05;
sigma2=0.02;
h1=-0.1865;
h2=0.7537;
r=0.02;   % real risk-free return
mu=0.04;  % equity risk premium
sigma=0.18; % volatility of equity return
beta=0.96; % discount factor
cr=0.15;   % contribution rate
w=0.5;     % weight of interim target
a=15.8382; % price of annuity on retirement
x=21:65;   
Z(1,x)=randn(1,45);
Z(2,x)=randn(1,45);
hist(x,-1:.05:1)  % Notice the symmetry around point Mu
Z(1,x) = Z(1,x) + abs(min(Z(1,x))); % Move everything to the right
Z(2,x) = Z(2,x) + abs(min(Z(2,x))); % Move everything to the right
%%Return on risky assets
R(x)=r+mu-1/2*sigma^2+sigma*Z(1,x);
S(x)=1+h1*(-1+(x-20)/45)+h2*(-1+4*(x-20)/45-((3^1/2)*(x-20)/45).^2);
I(x)=rl+(S(x)-S(x-1))/S(x-1)+sigma1*Z(1,x)+sigma2*Z(2,x);
Y(20)=1;
for x=21:65
    Y(x)=Y(x-1)*exp(I(x));
end
function F = myfun(teta)
F(x)=(F(x-1)+cr*Y(x-1))*exp(r+teta(x-1)*((mu-1/2*sigma.^2)+sigma*Z(1,x)));
teta=fminbnd(@myfun,0,1);
end

[Walter Roberson]

   F(x)=(F(x-1)+cr*Y(x-1))*exp(r+teta(x-1)*((mu-1/2*sigma.^2)+sigma*Z(1,x)))

defines F in terms of itself. You need to have a stopping condition, such as if you had a known F(1)

However, you never use myfun. The only reference to myfun is within myfun.

Perhaps F(x) is intended to be an array that you extend as you run? If so then you still need to know the first value to use. You do not try to store the value anywhere.

... Suppose you had done the minimization and found the best teta. What would you do with it?

[parisa lotfi]

In fact my model is stochastic dynamic programming and F one parts of the model. I try to write matlab codes model in the article that I attached it.

[Image Analyst]

Attached it? Attached it where?

http://matlab.wikia.com/wiki/FAQ#Can_you_program_up_the_algorithm_in_this_article_for_me_and_explain_it_to_me.3F

[parisa lotfi]

the name of article is :Target-Driven Investing: Optimal Investment Strategies in Defined Contribution Pension Plans Under Loss Aversion

[parisa lotfi]

Can anyone help me the subject in the previous comment??

[Walter Roberson]

Re-read section 2.3.1 on page 10 of the PDF. It makes it clear that F sub x is the value at the positive integer age x, and that the starting investment is to be 0. Your F should not be a recursive function, it should be a vector that you build up in a loop.

start_age = 20;
end_age = 85;

F = zeros(1, end_age);

for x = start_age+1 : end_age
  F(x) = (F(x-1)+cr*Y(x-1))*exp(r+teta(x-1)*((mu-1/2*sigma.^2)+sigma*Z(1,x)));
end

[parisa lotfi]

I reaally appreciate your help. there are two unknown parameters in this function( F(x) and teta) , and we have to find teta from part 2.5 on page 14 article , and don't know how can I write it. could any one possibly help me?

[parisa lotfi]

The codes related to that article that I attached in previous comments which implement in MATLAB are below. but there are errors. could any one help me?

%%Baseline Parameters
%%loss aversion parameters
lambda=4.5;  % loss aversion ratio
nu1=0.44;    % curvature parameter for gains
nu2=0.88;    % curvature parameter for loss
%%Labour income
rl=0.02;
sigma1=0.05;
sigma2=0.02;
h1=-0.1865;
h2=0.7537;
%%Asset returns
r=0.02;   % real risk-free return
mu=0.04;  % equity risk premium
sigma=0.18; % volatility of equity return
beta=0.96; % discount factor
%%other parameters
cr=0.15;   % contribution rate
w=0.5;     % weight of interim target
a=15.8382; % price of annuity on retirement
rstar= 3.1;
%%Define distributed standard normal random variables
x=21:65;   
Z(1,x)=randn(1,45);
Z(2,x)=randn(1,45);
hist(x,-1:.05:1)  % Notice the symmetry around point Mu
Z(1,x) = Z(1,x) + abs(min(Z(1,x))); % Move everything to the right
Z(2,x) = Z(2,x) + abs(min(Z(2,x))); % Move everything to the right
%%Return on risky assets
R(x)=r+mu-1/2*sigma^2+sigma*Z(1,x);
%%Career salary profile
S(x)=1+h1*(-1+(x-20)/45)+h2*(-1+4*(x-20)/45-((3^1/2)*(x-20)/45).^2);
 Labour income function &  Setting the final target
I(x)=rl+(S(x)-S(x-1))/S(x-1)+sigma1*Z(1,x)+sigma2*Z(2,x);
Y(20)=1;
for x=21:65
    Y(x)=Y(x-1)*exp(I(x));
end
start_age = 20;
end_age = 65;
expectedY=zeros(1,end_age);   
 y=cumsum(Y);
 for i=1:45
 expectedY=y./i;
 f=62.66*Y./expectedY;
 f=[zeros(1,19) f(20:65)];
 end 
 for s= 64:-1: start_age
     expectedYs=[zeros(1,19) expectedY(end:-1:20)];
     f(s+1)=[f(s)+cr*expectedYs]*(1+rstar);
 end
start_age = 20;
end_age = 65;
F = zeros(1, end_age);
F(20)=0;
teta(20)=0;
for x = start_age+1 : end_age
  F(x) = (F(x-1)+cr*Y(x-1))*exp(r+teta(x-1)*((mu-1/2*sigma.^2)+sigma*Z(1,x)));
end
%%reward matrix
function U=reward(F,f,lambda,nu1,nu2)
n=length(F);
m=length(f);
U=zeros(n,m);
for i=1:n
    for k=1:m
        if f(k)< F(i)
           U(i,k)= -lambda*((f(k)-F(i))^nu2)/nu2 ;
        else
            U(i,k)=((F(i)-f(k))^nu1)/nu1;
        end
    end
end
% transition matrix  g
function g=transition(F,f)
n=length(F);
m=length(f);
g=zeros(n,m);
for i=1:n
    for k=1:m
        Fnext=F(i)-f(k);
        if Fnext<=0;
            Fnext=0;
        end
        g(i,k)=find(F==Fnext);
    end
end
%%function iteration
function dp(U,g,v)
[n,m]= size(U);
for i=1:10
    p=sparse(1:n*m , g(:) ,1 , n*m ,n)*v;
    pp=reshape(p,n,m);
    ppp=U+0.96*pp;
    [vnew,fstar]=max( ppp, [] ,2);
    if abs(vnew(n)-v(n))<=10^(-6),break,end
    v=vnew
    fstar
    endv=vnew
    fstar

      % code
    end

[Walter Roberson]

You do not appear to use function dp?

[parisa lotfi]

yes, but I don't know what should I do