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 Delbaen and Schachermayer (Math Finance 4:343-348, 1994). We also provide no arbitrage conditions for stochastic processes within the class of simple trading strategies with shortsale restriction.