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Quantitative Finance

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  • $\begingroup$ Won thank you very much for your explanation.it is perfect and full of detail. $\endgroup$ Commented Oct 25, 2014 at 14:12
  • $\begingroup$ can you please tell me how you get your $G=e^{-rt}F$? $\endgroup$ Commented Oct 25, 2014 at 14:15
  • $\begingroup$ That's a general method to make the original PDE easier. Just substitute $F = e^{rT} G$ into the PDE and you will get a new PDE in terms of $G$. This PDE is the same as the old one, but without the $rF$ term. So we then perform the same manipulations for $G$, obtain the final result and then transform the final expression back to $F$. $\endgroup$ Commented Oct 25, 2014 at 19:26
  • $\begingroup$ Just wondering how this looks if you have a PDE with two spatial variables, for instance x and y, i.e $\mu_1x\displaystyle\frac{\partial F}{\partial x} + \mu_2y\displaystyle\frac{\partial F}{\partial y} + \displaystyle\frac{1}{2}\sigma_1^2 \displaystyle\frac{\partial^2 F}{\partial x^2} + \displaystyle\frac{1}{2}\sigma_2^2 \displaystyle\frac{\partial^2 F}{\partial y^2} $ =rF(x,y) ? $\endgroup$ Commented Nov 25, 2018 at 12:38