Question about fsolve
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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)
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採用された回答
Sargondjani
2012 年 6 月 25 日
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)
その他の回答 (1 件)
Sargondjani
2012 年 6 月 21 日
first of all you should delete the /M in the objective, because this only scales your problem in a bad way. another problem could arise when Rs-Rf is very close to zero, because then the objective will get very close to zero, no matter what omega is (and will thus appear singular)
does your problem solve when you have just one random element in Z, a and a_1?
actually im also a bit confused in what you are trying to do:
- - before you had an omega for every element and then there is a solution for every element, but now with only one omega for all elements, there is no solution W(:)=0 (minimizing least squares seems more appropriate in that case)
- -also i see time variables, but you dont do anything with (R,dt,N,t,T)
- -what are 'a' and 'a_1', because I am surprised that thoser random numbers enther the objective as well (the random market return i can understand)
3 件のコメント
Sargondjani
2012 年 6 月 23 日
This is not a problem. Like it says the equation is solved! (any further improvements are smaller than the stopping criteria)
but i still wonder if you got what you want.... if you have properly defined the problem
what do you mean with "I want to solve an individual optimal question" because now there is still only one value for omega. and a and a_1 ARE random numbers...
... and still nothing happens with your time variables
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