No-Arbitrage Conditions for Strict Local Martingales and Simple Strategies

Summary

This theoretical article studies when strict local martingales can support arbitrage under simple trading strategies. Its setup excludes doubling strategies and does not impose a lower bound on losses, so its conclusions depend on a particular and relatively permissive trading framework. The central result is that, for a class of nonnegative strict local martingales, the strong Markov property implies no arbitrage for simple strategies. This extends a related result for the three dimensional Bessel process.

The article also gives no-arbitrage conditions for stochastic processes when short selling is restricted. The excerpt states mathematical conclusions but does not specify the full assumptions, proof techniques, or practical market model. The results are therefore useful as a framework for understanding how strategy constraints and process properties affect arbitrage claims, rather than as direct evidence about a tradable market. In particular, the conclusions should not be generalized beyond the stated classes of processes and strategies without checking their conditions.

Key ideas

• Strict local martingales can admit arbitrage under some classes of simple strategies.
• For a stated class of nonnegative strict local martingales, the strong Markov property yields no arbitrage.
• The result generalizes a related finding for the three dimensional Bessel process.
• The framework rules out doubling strategies but does not require losses to have a lower bound.
• Short sale restrictions lead to additional process conditions for no arbitrage.

Tags

# No Arbitrage Conditions For Simple Trading Strategies


# No Arbitrage Conditions For Simple Trading Strategies









Strict local martingales may admit arbitrage opportunities with respect to the class of simple trading strategies. (Since there is no possibility of using doubling strategies in this framework, the losses are not assumed to be bounded from below.) We show that for a class of non-negative strict local martingales, the strong Markov property implies the no arbitrage property with respect to the class of simple trading strategies. This result can be seen as a generalization of a similar result on three dimensional Bessel process in [3]. We also pro- vide no arbitrage conditions for stochastic processes within the class of simple trading strategies with shortsale restriction.

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