finance Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of fina ...

, 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, consistency ...

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 Market value, value of the asset falls. This is the opposite of a more conventional "Long (finance), long" Position (finance), position, wh ...

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

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 ra ...

(and therefore

\bar

is the

discounted price The net present value (NPV) or net present worth (NPW) applies to a series of cash flows occurring at different times. The present value of a cash flow depends on the interval of time between now and the cash flow. It also depends on the discount ...

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

References

{{finance stub Mathematical finance