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(Just what I think is the right start) The pricing PDE comes out of the dynamics of a self-financing portfolio, $\Pi$, hedged against the movements of stock, $S$, its volatility, $v$, and interest rate $r$. With $V$ the target path-independent derivative, $U$ vanilla European option (different from $V$), and $P$ zero-coupon bond, the portfolio would be: $$ \...

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