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Math · Advanced Math
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Conversion of the Black-Scholes Equation to the Diffusion Equation We first bring the equation into the standard form of the diffusion equation, and then solve it using the Greens function for the diffusion equation on the initial condition at T he ist di erence we notice rom the canonical equation is that the coe icients depend on x However, the equation is homogeneous or variant under the scaling of x → ar he standard way to simplitv this and eliminate the explicit coordinate dependence is to detine a new variable al- n(z/c), where we have scaled x by c to make it dimensionless. Then under r → ar u → u In a since the equation is invariant under this it cannot have an explicit dependence on in the coe icients. Chan n variables t ising 스 ↓ and detinin er a t w z t tede vatives come

This is a screenshot of a paper I have been reading. Could you please explain how the author arrived at equation 8. Many thanks and I will remember to up vote for response (of course, only if it makes sense).

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