Mean‐reverting discrete time market models: speculative opportunities and absence of arbitrage

In this article, we study discrete time mean‐reverting market models. We show that certain choices of initial conditions ensure existence of an equivalent martingale measure and absence of arbitrage for any finite time horizon. Further, it is shown that this model still allows some speculative opportunities. These opportunities cannot be expressed in the terms of arbitrage or asymptotic arbitrage. In particular, a gain can be achieved for a wide enough set of expected utilities for a strategy that does not require any hypothesis on market parameters and does not use estimation of these parameters.