Originally Posted by
Tribal5 I'm trying to work out the following Cauchy-Euler problem, was hoping someone could help
the equation is:
1/2*J*s^2 v'' + (r -D)S v' - rV =0, for 0<S<A
V(s) = S - E, for s>a
when V(0) = 0 , V(A) = A - E, dV/dS = 1
I've to show v(s) = (A - E)(S/A)^m
where m = 1/J * [-(r-D-J/2) + Sqrt( (r-D-J/2)^2 + 2rJ))
note J = Sigma^2 (Sorry don't know how to use LaTeX)
I can work out m using V = S^{m } and i guess the root is v = C_{1}S^{m} + C_{2}S^{m }
But i just can't tie it all together, any ideas?