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.[1] A typical example of a trading strategy which is not admissible is the doubling strategy.[2]

Mathematical definition

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Discrete time

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In a market with   assets, a trading strategy   is admissible if   is almost surely bounded from below. In the definition let   be the vector of prices,   be the risk-free rate (and therefore   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

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Let   be a d-dimensional semimartingale market and   a predictable stochastic process/trading strategy. Then   is called admissible integrand for the semimartingale   or just admissible, if

  1. the stochastic integral   is well defined.
  2. there exists a constant   such that  .[3]

References

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  1. ^ a b Föllmer, Hans; Schied, Alexander (2004). Stochastic finance: an introduction in discrete time (2 ed.). Walter de Gruyter. pp. 203–205. ISBN 9783110183467.
  2. ^ a b Frank Oertel; Mark Owen (2006). "On utility-based super-replication prices of contingent claims with unbounded payoffs". arXiv:math/0609403.
  3. ^ Delbaen, Schachermayer (2008). The Mathematics of Arbitrage (corrected 2nd ed.). Berlin Heidelberg: Springer-Verlag. p. 130. ISBN 978-3-540-21992-7.