Solution
= Solution
An $x$-admissible strategy is a predictable vector of holdings $\phi=(\phi^0,\ldots,\phi^d)$ that is integrable against the asset prices, is <self-financing portfolio>[self-financing], has initial wealth
$$
V_0=\sum_i\phi_0^iS_0^i=x,
$$
and whose wealth process $V_t=\sum_i\phi_t^iS_t^i$ remains nonnegative.