Julia: NLsolve providing different solution each run and sometimes returns NaN?

Hi,

Note: I have cross-posted this to stackexchange: https://stackoverflow.com/questions/62619689/julia-nlsolve-providing-different-solution-each-run-and-sometimes-returns-nan

I am trying to replicate some matlab code as a part of my master thesis from the paper Zhu, H. (2014). Do dark pools harm price discovery?

I have a system of two equations which i solve using the “NLsolve” package in Julia. The issue is that NLsolve returns a different solution for f[1] each time i run the code and sometimes it returns a “NaN”.

I am not sure what is causing this?

Here is a code excerpt:

using NLsolve;

function G(x)
    min(1,x/C)
end;

function Ginv(x)
    min(C,x*C) 
end;

function F(x)
    1-exp(-x/2)
end;

μᵤ = 60;
σᵤ = sqrt(μᵤ);
a = [0 0];
b = [3*μᵤ 3*μᵤ];
r_bar = 0.91;
μ_bar  = 20;
C = 2;
x₀ = [μ_bar, 1.0];

function f_temp!(x,f)
   f[1] = μ_bar*F((1-G(1))*μᵤ*x[2]/(x[1]+(1-G(1))μᵤ))-x[1]
   f[2] = 1-x[1]/(x[1]+(1-G(1))μᵤ)-r_bar
end;

x = nlsolve(f_temp!, x₀)

μ_hat₀ = x.zero[1];
σ₀ = x.zero[2];

In the second part of my code i think the same issue with “NLsolve” persists and causes the error “During the resolution of the non-linear system, the evaluation of the following equation(s) resulted in a non-finite number: [1]”

σ = exp.([LinRange(log(0.02),log(σ₀),30) 
          LinRange(log(σ₀*1.1),log(70),20)]);
K = length(σ);

α₀ = fill(NaN,(K,2));
αₑ = fill(NaN,(K,2);
μᵢ = fill(NaN,(K,2));

function func!(x,f)
    f[1] = x[2]/(x[2]+x[1]*μᵤ)-Ginv(1-x[1])
    f[2] = μ_bar*F(x[1]*μᵤ*σₙ/(x[2]+x[1]*μᵤ))-x[2]
end;

for n=1:K
    global σₙ 
    σₙ = σ[n] 
    
   if n==1
        x = nlsolve(func!,[1-G(1), μ_bar])
    else
        x = nlsolve(func!,[real(αₑ[n-1,1]),  μ_bar])
    end
    
    αₑ[n,1] = x.zero[1]
    α₀[n,1] = 1-αₑ[n,1]
    μᵢ[n,1] = x.zero[2]
    end;

All help appreciated.

Best regards,
Rasmus

I have solved the issue with help from stackoverflow. How do i delete this post?

Best regards,
Rasmus