Originally Posted by

**hypokrit** Hi all !

I have not very spectucular function

and

I need to get with an initial value x(1), which I dont know yet, a sum of e.g. 10. I "programmed" a loop and find empirically an initial value of 9.47 to get a sum of 10 for this function (with 10 time steps). But this is either a sophisticated nor a mathematical solution.

here the function:

a=4 %phi, mean reversion

s=1 %local volatility

n=10 %years, time steps

x(1)=?

for i=2:n

x(i)=4*x(i-1)*s^2/(1+sqrt(1+4*x(i-1)*a*s^2))^2

end

out=sum(x)

Do you need bisections methods ? If yes, how I implement one for this ?

I am not a mathematicien so I would be very gratefull for any suggestions !

Thanks a lot in advance !

Recode this as a function ff(x) where x will be the initial value and ff(x)=0 when your sum is 10. so something like this:

Code:

function rv=ff(x0)
a=4 %phi, mean reversion
s=1 %local volatility
n=10 %years, time steps
x=zeros(1,10);
x(1)=x0;
for i=2:n
x(i)=4*x(i-1)*s^2/(1+sqrt(1+4*x(i-1)*a*s^2))^2
end
rv=sum(x)-10;

Now you use a numerical root finder on this.

CB