\begin{equation} \label{eq:implicit_oneTrade}
    \begin{bmatrix} 
    1 & -2 & 1 & 0 & \dots \\
    a_2 & b_2 & c_2 & 0 & \dots \\
    0 & a_3 & b_3 & c_3 & 0 & \dots \\
    \vdots & \ddots & \ddots &\ddots & \ddots & \ddots \\ \\
    0 & \dots & & & a_{J-1} & b_{J-1} & c_{J-1} \\
    0 & \dots & & 0 & 1 & -2 & 1
    \end{bmatrix}
    \begin{bmatrix}
           U^{\star}_{k-1,i,1} \\
           U^{\star}_{k-1,i,2} \\
           U^{\star}_{k-1,i,3} \\
           \vdots \\ \\
           U^{\star}_{k-1,i,J-1} \\
           U^{\star}_{k-1,i,J}
         \end{bmatrix}
    =
    \begin{bmatrix}
           0 \\
           H_{k,i,2} \\
           H_{k,i,3} \\
           \vdots \\ \\
           H_{k,i,J-1} \\
           0
         \end{bmatrix}
\end{equation}
