  We consider a $d-$dimensional insurance network, with initial capital
$a\in\R^d_+,$ operating under a risk diversifying treaty; this is described in
terms of a regulated random walk $\{Z^{(a)}_n\}$ via Skorokhod problem in
$\R^d_+$ with reflection matrix $R;$ $\{Y^{(a)}_n\}$ denotes the corresponding
pushing process. Ruin (in a strong sense) of $\{Z^{(a)}_n\}$ is defined as the
marginal deficit of each company being positive (and hence zero surplus) at
some time $n.$ A dual storage network is introduced through time reversal at
sample path level over finite time horizon; the stochastic analogue is again a
regulated random walk $\{W_n\}$ in $\R^d_+$ starting at $0.$ It is shown that
ruin for $\{Z^{(a)}_n\}$ corresponds to $\{W_n\}$ hitting open upper orthant
determined by $R^{-1}a$ before hitting the boundary of $\R^d_+,$ even at the
sample path level. Under natural hypotheses, we show that $\P($ ruin of
$\{Z^{(a)}_n\}$ in finite time) $=\lim_{n\r\iy}\P(W_n\gg R^{-1}a: n<$ boundary
hitting time of storage process) $=\lim_{n\r\iy}\P(Y^{(0)}_n \gg R^{-1}a:\Delta
Y^{(0)}_n\gg 0).$ A notion of $d-$dimensional ladder height distribution is
defined, and a Pollaczek-Khinchine formula derived; an expression for the
ladder height distribution is presented. Our method is applicable to ruin
problem for a continuous time $d-$dimensional Cramer-Lundberg type network,
where the companies act independently in the absence of treaty.
