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Hi everyone,

I am doing a sheet on Asian Options and The Black Scholes equation.

I have the PDE,

[itex]\frac{∂v}{∂τ}[/itex]=[itex]\frac{1}{2}[/itex][itex]σ^{2}[/itex][itex]\frac{X^{2}}{S^{2}}[/itex][itex]\frac{∂^{2}v}{∂ε^{2}}[/itex] + ([itex]\frac{1}{T}[/itex] + (r-D)X)[itex]\frac{∂v}{∂ε}[/itex]

I have to seek a solultion of the form v=[itex]α_{1}[/itex](τ)ε + [itex]α_{0}[/itex](τ) and determine the general solution for [itex]α_{1}[/itex](τ) and [itex]α_{0}[/itex](τ).

We are given that ε=[itex]\frac{I}{TS}[/itex] - [itex]\frac{X}{S}[/itex], τ=T-t and V(S, I, t)=[itex]e^{-Dτ}[/itex]Sv(ε, τ)

Can anybody help me with this problem?

Thanks

I am doing a sheet on Asian Options and The Black Scholes equation.

I have the PDE,

[itex]\frac{∂v}{∂τ}[/itex]=[itex]\frac{1}{2}[/itex][itex]σ^{2}[/itex][itex]\frac{X^{2}}{S^{2}}[/itex][itex]\frac{∂^{2}v}{∂ε^{2}}[/itex] + ([itex]\frac{1}{T}[/itex] + (r-D)X)[itex]\frac{∂v}{∂ε}[/itex]

I have to seek a solultion of the form v=[itex]α_{1}[/itex](τ)ε + [itex]α_{0}[/itex](τ) and determine the general solution for [itex]α_{1}[/itex](τ) and [itex]α_{0}[/itex](τ).

We are given that ε=[itex]\frac{I}{TS}[/itex] - [itex]\frac{X}{S}[/itex], τ=T-t and V(S, I, t)=[itex]e^{-Dτ}[/itex]Sv(ε, τ)

Can anybody help me with this problem?

Thanks

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