1$\
$\sum_{j = 1}^n \pi_{ji}(1)p_j(1)$]{};

(3,5) rectangle (6,9) node\[pos=.5,style=[align=center]{}\][Cash-Flow @ $t = 0$\
$\sum_{j = 1}^n L_{ij}(0)$]{}; (3,1.5) rectangle (6,5) node\[pos=.5,style=[align=center]{}\][Cash-Flow @ $t = 1$\
$\sum_{j = 1}^n L_{ij}(1)$]{}; (3,0) rectangle (6,1.5) node\[pos=.5,style=[align=center]{}\][Capital\
$V_i(1)$]{};

(0,0) rectangle (3,9); (3,0) rectangle (6,9);

(0,7) – (3,7); (0,6) – (3,6); (0,2) – (3,2); (3,5) – (6,5);

 \

(0,6.5) rectangle (6,7) node\[pos=.5\][**Balance Sheet @ $t = 0$**]{}; (0,6) rectangle (3,6.5) node\[pos=.5\][**Assets**]{}; (3,6) rectangle (6,6.5) node\[pos=.5\][**Liabilities**]{};

(0,4) rectangle (3,6) node\[pos=.5,style=[align=center]{}\][Cash-Flow\
$x_i(0)$]{}; (0,0) rectangle (3,4) node\[pos=.5,style=[align=center]{}\][Interbank\
$\sum_{j = 1}^n \pi_{ji}(0)p_j(0)$]{};

(3,2) rectangle (6,6) node\[pos=.5,style=[align=center]{}\][Cash-Flow\
$\sum_{j = 1}^n L_{ij}(0)$]{}; (3,0) rectangle (6,2) node\[pos=.5,style=[align=center]{}\] (t) [Capital\
$V_i(0)$]{};

(7,6.5) rectangle (13,7) node\[pos=.5\][**Balance Sheet @ $t = 1$**]{}; (7,6) rectangle (10,6.5) node\[pos=.5\][**Assets**]{}; (10,6) rectangle (13,6.5) node\[pos=.5\][**Liabilities**]{};

in [0.5]{}

(7,4+) rectangle (10,5+) node\[pos=.5,style=[align=center]{}\][Cash-Flow\
$x_i(1)$]{}; (7,2+) rectangle (10,4+) node\[pos=.5,style=[align=center]{}\] (t+1) [Carry-Forward\
$V_i(0)^+$]{}; (7,0+) rectangle (10,2+) node\[pos=.5,style=[align=center]{}\][Interbank\
$\sum_{j = 1}^n \pi_{ji}(1)p_j(1)$]{};

(10,1.5+) rectangle (13,5+) node\[pos=.5,style=[align=center]{}\][Cash-Flow\
$\sum_{j = 1}^n L_{ij}(1)$]{}; (13.2,1+) rectangle (16,2+) node\[pos=.5,style=[align=center]{}\][Carry-Forward\
$V_i(0)^- = 0$]{}; (13,1.5+) – (13.2,2+) – (13.2,1+) – cycle; (13,1.5+) – (13.2,2+) – (16,2+) – (16,1+) – (13.2,1+) – cycle; (10,0+) rectangle (13,1.5+) node\[pos=.5,style=[align=center]{}\][Capital\
$V_i(1)$]{}; (6,1) – (7,3+); (6,.25) – (14,.25) – (14,1+);

In this setting, we will consider the external (incoming) cash flow $x: {\mathbb{T}}\to {\mathbb{R}}^{n+1}_+$ and nominal liabilities 