Plan designed to achieve profitable return
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.
Mathematical definition.
Discrete time.
In a market with formula_1 assets, a trading strategy formula_2 is "admissible" if formula_3 is almost surely bounded from below. In the definition let formula_4 be the vector of prices, formula_5 be the risk-free rate (and therefore formula_6 is the discounted price).
In a model with more than one time then the wealth process associated with an admissible trading strategy must be uniformly bounded from below.
Continuous time.
Let formula_7 be a d-dimensional semimartingale market and formula_8 a predictable stochastic process/trading strategy. Then formula_9 is called "admissible integrand for the semimartingale" formula_4 or just "admissible", if
References.
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