Check that the function $g(t, x)$ in (11.26) satisfies the boundary conditions
$$
\left\{\begin{array}{l}
g(t, B)=0, \quad t \in[0, T] \\
g(T, x)=0, \quad x \leqslant Kg(T, x)=x-K, \quad K \leqslant xg(T, x)=0, \quad x>B
\end{array}ight.
$$