Admissible trading strategy

In finance, an admissible trading strategy or admissible strategy is any trading strategy with wealth almost surely bounded from below. In particular, an admissible trading strategy precludes unhedged short sales of any unbounded assets. A typical example of a trading strategy which is not admissible is the doubling strategy.

In a market with ${\displaystyle d}$ assets, a trading strategy ${\displaystyle x\in \mathbb {R} ^{d}}$ is admissible if ${\displaystyle x^{T}{\bar {S}}=x^{T}{\frac {S}{1+r}}}$ is almost surely bounded from below. In the definition let ${\displaystyle S}$ be the vector of prices, ${\displaystyle r}$ be the risk-free rate (and therefore ${\displaystyle {\bar {S}}}$ is the discounted price).

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