# Black-Scholes PDE：邊界條件的形式是什麽

I'm working on the Black-Scholes equation, but I'm pretty new to financial modeling. Right now, I am trying to understand the Black-Scholes PDE. I understand that the Black-Scholes equation is given by \begin{equation*} \frac{\partial C}{\partial t} + \frac{1}{2}\sigma^2 S^2\frac{\partial^2 C}{\partial S^2} + rS \frac{\partial C}{\partial S} - rC = 0 \end{equation*} with initial condition \begin{equation*} C(S,T) = \max (S-K, 0) \end{equation*} and boundary conditions \begin{equation*} C(0,t) = 0 \hspace{35pt} C(S,t) \rightarrow S \text{ as } S \rightarrow \infty \end{equation*} and $C(S,t)$ is defined over $0 < S < \infty$, $0 \leq t \leq T$.

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