Follow this paper : http://www.math.ku.dk/~hugger/articles/CTAC2003.pdf
Let \begin{equation}\mathcal{L}V=\displaystyle\frac{1}{2}\sigma^2S^2\frac{\partial^2 V}{\partial S^2}
+rS\displaystyle\frac{\partial V}{\partial S}
+\displaystyle S\frac{\partial V}{\partial A}-rV
\end{equation}
Let \begin{equation}\Omega\end{equation} be an unbounded subset of \begin{equation}\mathbb{R}^2\end{equation}. Consider the boundary condition for a put option:
\begin{equation}
\left\{\begin{array}{ll}
V(S,A,0)=\max\left\{K-\frac{A}{T},0 \right\},\\
V(0,A,t)=e^{-rt}\max\left\{K-\frac{A}{T},0 \right\},\\
V(S,A,t)=e^{-rt} (K-\frac{A}{T} )+\frac{S}{rT}(1-e^{-rt}),\;\text{for}\;I\leq KT,\\
V(S_{\max},A,t)\simeq \max\left\{ e^{-r_it}(K-\frac{A}{T} )+\frac{S_{max}}{rT}(1-e^{-rt}),0\right\}
\end{array}\right.
\end{equation}
My question is: Do I have a correct condition for put option? If I am wrong, what should be changed ?
I have been searching for this result but I have not found one. Thanks for your time.
Let \begin{equation}\mathcal{L}V=\displaystyle\frac{1}{2}\sigma^2S^2\frac{\partial^2 V}{\partial S^2}
+rS\displaystyle\frac{\partial V}{\partial S}
+\displaystyle S\frac{\partial V}{\partial A}-rV
\end{equation}
Let \begin{equation}\Omega\end{equation} be an unbounded subset of \begin{equation}\mathbb{R}^2\end{equation}. Consider the boundary condition for a put option:
\begin{equation}
\left\{\begin{array}{ll}
V(S,A,0)=\max\left\{K-\frac{A}{T},0 \right\},\\
V(0,A,t)=e^{-rt}\max\left\{K-\frac{A}{T},0 \right\},\\
V(S,A,t)=e^{-rt} (K-\frac{A}{T} )+\frac{S}{rT}(1-e^{-rt}),\;\text{for}\;I\leq KT,\\
V(S_{\max},A,t)\simeq \max\left\{ e^{-r_it}(K-\frac{A}{T} )+\frac{S_{max}}{rT}(1-e^{-rt}),0\right\}
\end{array}\right.
\end{equation}
My question is: Do I have a correct condition for put option? If I am wrong, what should be changed ?
I have been searching for this result but I have not found one. Thanks for your time.
