Hello,
I have the function f(t,S) defined as follows:
f(t,S):=exp(-r*(T-t))*(log(S)+(r-(sigma^2)/2)*(T-t))
I need to prove that f(t,S)*r is a solution to the following differential
equation:
diff(f(t,S),t)+r*S*diff(f(t,S),S)+(1/2)*sigma^2*S^2*diff(f(t,S),S,2)
Once I get this (by inputing the two above lines of code):
r*((r-sigma^2/2)*(T-t)+log(S))*%e^(-r*(T-t))-(sigma^2*%e^(-r*(T-t)))/2+(sigma^2/2-r)*%e^(-r*(T-t))+r*%e^(-r*(T-t))
I don't know how to proceed. Somehow, I would like Maxima to isolate f(t,S)
and instead giving me the above formula it would give me: f(t,S)*r as a
result.
Please advise. Any comment welcome.
Thanks in advance,
Julien.