In finance, an admissible trading strategy or admissible strategy is any

trading strategy In finance, a trading strategy is a fixed plan that is designed to achieve a profitable return by going long or short in markets. The main reasons that a properly researched trading strategy helps are its verifiability, quantifiability, consiste ...

with wealth

almost surely In probability theory, an event is said to happen almost surely (sometimes abbreviated as a.s.) if it happens with probability 1 (or Lebesgue measure 1). In other words, the set of possible exceptions may be non-empty, but it has probability 0 ...

bounded from below. In particular, an admissible trading strategy precludes unhedged

short sales In finance, being short in an asset means investing in such a way that the investor will profit if the value of the asset falls. This is the opposite of a more conventional " long" position, where the investor will profit if the value of th ...

of any unbounded assets. A typical example of a trading strategy which is not ''admissible'' is the

doubling strategy Doubling may refer to: Mathematics * Arithmetical doubling of a count or a measure, expressed as: ** Multiplication by 2 ** Increase by 100%, i.e. one-hundred percent ** Doubling the cube (i. e., hypothetical geometric construction of a cube w ...

Mathematical definition

In a market with

d

assets, a trading strategy

x \in \mathbb^d

is ''admissible'' if

x^T \bar = x^T \frac

is almost surely bounded from below. In the definition let

S

be the vector of prices,

r

be the

risk-free rate The risk-free rate of return, usually shortened to the risk-free rate, is the rate of return of a hypothetical investment with scheduled payments over a fixed period of time that is assumed to meet all payment obligations. Since the risk-free r ...

(and therefore

\bar

is the discounted price). In a model with more than one time then the

wealth process Wealth is the abundance of valuable financial assets or physical possessions which can be converted into a form that can be used for transactions. This includes the core meaning as held in the originating Old English word , which is from an I ...

associated with an admissible trading strategy must be uniformly bounded from below.

References

{{finance stub Mathematical finance