MATLAB: Question about fsolve

fsolveOptimization Toolbox

After reading the answer of my last question, I change my code about fsolve, but there is still notification of: No solution found.
fsolve stopped because the problem appears to be locally singular.
<stopping criteria details>
Would anyone could check my code and give me some advises plz? Thanks a lot.:
%%function for omega of every time period for OI scheme
function f=function_1_5_3(x,Z)
r0=.02;%interest rate
sigma=.15;%vatality rate of risky asset
mu0=.06;%drift rate of risky asset
gamma=5;%risk aversion rate
M=10000;%number of trajectories
N=55;%time period
T=55;%total time period
R=40;%time of retirement
dt=T/N;%each time period
t=1:dt:T;
omega=x;
Rf=exp(r0);%riskless reture
load OI_a_matrix;%set a grid of at
Rs=exp(mu0+sigma*Z);%risky market return
a=20*mat(:,N-2);
a_1=20*mat(:,N-1);
W=((a.*(Rf+omega*(Rs-Rf))-a_1).^(-gamma)).*(Rs-Rf)/M;
f=W;
and
clear
M=10000;
x0=0.4;
Z=randn(M,1);
x=fsolve(@(x)function_1_5_3(x,Z),x0)
in which the loaded matrix is a random matrix which saved at first:
mat=rand(M,N)

Best Answer

first you should try yourself to solve the equation when there is just 1 line (1 a and a_1). see what's happening... and then increase to a couple of lines.
and it seem there is no (serial) correlation between a and a_1, so why not just use their expected values??? (im not a statics expert, but if they are not correlated it think that is a fair thing to do)
i will try to help with limited time, but then i first need to understand better what you want to do in words: what is the equation? do you have documentation on it? because i still find the equation obscure. i especially want to know what 'a' and a_1 and omega are (in words)
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