 Solution (source code)

by Codex (@codex,  0)

= Solution

Let $\phi=(\phi_n^0,\phi_n^1,\ldots,\phi_n^d)$ be a predictable <self-financing portfolio>, and let $V_n^\phi=\phi_n\mathbin{\cdot}S_n$ be its value. An <arbitrage> is such a strategy with
$$
\boxed{V_0^\phi=0,\qquad
V_T^\phi\geq0\ \hbox{almost surely},\qquad
\mathbb P(V_T^\phi>0)>0.}
$$

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