[Maxima] Applying Ito's lemma

Barton Willis willisb at unk.edu
Thu Jun 4 08:05:08 CDT 2009


When I tried your calculation, I got

 (%o18) dt*('diff(f(t),t,2)/f(t)-('diff(f(t),t,1))^2/f(t)^2+
 (sigma_f*sigma_g+r)/f(t)-sigma_f^2/2)+dz*sigma_f

What is wrong with (%o18)? In general, derivatives with respect to
non-symbols
(for example, diff(g(f,t),f(t),1)) might not work, but it seems to be OK
for this
calculation.

Barton

-----maxima-bounces at math.utexas.edu wrote: -----


>Here is what I tried:
>
>g(f,t):=log(f(t));
>
>(diff(g(f,t),f(t),1)*(r + sigma_f * sigma_g) + diff(g(f,t),t,2) + 1/2*
>diff(g(f,t),f(t),2)*(sigma_f * f(t))^2)*dt + diff(g(f,t),f(t),1)*(sigma_f
>* f(t))*dz;

>I don't get what I want i.e. I it does not seem to derive. What I am
>getting wrong in the syntax?
>
>Can anyone please help?




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