= Admissible trading strategy
An <admissible trading strategy> is a permitted stochastically integrable trading rule satisfying the model's wealth restriction. A common finite-horizon convention, relative to a fixed positive <numéraire> $B$, requires a deterministic $a\ge0$ such that
$$
V_t/B_t\ge-a\qquad\text{for all }t\le T.
$$
The bound may depend on the strategy. Nonnegative wealth is sufficient. The choice of <numéraire> and whether the restriction is imposed on nominal or discounted wealth must be stated; the corresponding conditions need not agree for an arbitrary random account.
Under an <equivalent local martingale measure>, discounted <self-financing> gains are <local martingales>. The deterministic lower bound makes the discounted wealth a <supermartingale>, supporting the usual <no-arbitrage> and minimal-replication-cost arguments. Restrictions only on terminal wealth do not exclude all doubling strategies.
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