Discrete time

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).^[1]

In a model with more than one time then the wealth process associated with an admissible trading strategy must be uniformly bounded from below.^[2]

Continuous time

Let ${\displaystyle S=(S_{t})_{t\geq 0}}$ be a d-dimensional semimartingale market and ${\displaystyle H=(H_{t})_{t\geq 0}}$ a predictable stochastic process/trading strategy. Then ${\displaystyle H}$ is called admissible integrand for the semimartingale ${\displaystyle S}$ or just admissible, if

1. the stochastic integral ${\displaystyle H\cdot S}$ is well defined.
2. there exists a constant ${\displaystyle M\geq 0}$ such that ${\displaystyle (H\cdot S)_{t}\geq -M\,a.s.,\quad \forall t\geq 0}$.^[3]