Ergodic aspects of trading with threshold strategies

Abstract To profit from price oscillations, investors frequently use threshold-type strategies where changes in the portfolio position are triggered by some indicators reaching prescribed levels. In this paper we investigate context of ergodic control. We make first steps towards their optimization proving properties related functionals. Assuming Markovian increments satisfying a minorization condition and (one-sided) boundedness show, particular, that for given thresholds, distribution gains converges long run. also extend recent results on stability overshoots random walks i.i.d. increment case to increments, under suitable conditions.