We show that with suitable restrictions on allowable trading strategies, one has no arbitrage in settings where the traditional theory would admit arbitrage possibilities. In particular, price processes that are not semimartingales are possible in our setting, for example, fractional Brownian motion.Comment: Published in at http://dx.doi.org/10.1214/08-AAP554 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Under proportional transaction costs, a price process is said to have a consistent price system, if there is a semimartingale with an equivalent martingale measure that evolves within the bid-ask spread. We show that a continuous, multi-asset price process has a consistent price system, under arbitrarily small proportional transaction costs, if it satisfies a natural multi-dimensional generalization of the stickiness condition introduced by Guasoni [5].

Abstract. In this note, we study no-arbitrage conditions in a market with multiple risky assets and proportional transaction costs. We present a condition which is sufficient for the market to be arbitrage-free and investigate its properties. In particular, we provide examples of price processes that are not semimartingales but are consistent with absense of arbitrage.

In [4] the notion of stickiness for stochastic processes was introduced. It was also shown that stickiness implies absence of arbitrage in a market with proportional transaction costs. In this paper, we investigate the notion of stickiness further. In particular, we give examples of processes that are not semimartingales but are sticky.

Abstract. 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 provide no arbitrage conditions for stochastic processes within the class of simple trading strategies with shortsale restriction.