Black-Scholes PDE and finding the general solution

[meghibbert17]

Hello, I have the PDE

\frac{-∂v}{∂τ}+\frac{1}{2}σ^{2}ε^{2}\frac{∂^{2}v}{∂ε^{2}}+(\frac{1}{T}+(r-D)ε)\frac{∂v}{∂ε}=0

and firstly I need to seek a solution of the form v=α_{1}(τ)ε + α_{0}(τ) and then determine the general solution for α_{1}(τ) and α_{0}(τ).

I am given that ε=\frac{I}{TS} - \frac{X}{S} and that τ=T-t.

Can anybody help me with this problem?

Thankyou

 

[chiro]

Hello, I have the PDE

\frac{-∂v}{∂τ}+\frac{1}{2}σ^{2}ε^{2}\frac{∂^{2}v}{∂ε^{2}}+(\frac{1}{T}+(r-D)ε)\frac{∂v}{∂ε}=0

and firstly I need to seek a solution of the form v=α_{1}(τ)ε + α_{0}(τ) and then determine the general solution for α_{1}(τ) and α_{0}(τ).

I am given that ε=\frac{I}{TS} - \frac{X}{S} and that τ=T-t.

Can anybody help me with this problem?

Thankyou

Hey meghibbert17 and welcome to the forums.

Are you familiar with the idea for transforming the B.S. to a standard PDE heat equation?