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Admissible trading strategy

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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.