We consider a portfolio optimization problem in a Black-Scholes model with n stocks, in which an investor faces both fixed and proportional transaction costs. The performance of an investment strategy is measured by the average return of the corresponding portfolio over an infinite time horizon....

Guasoni (2006) introduced a simple condition for the absence of arbitrage opportunities. In this note we show that his results remain valid under a weaker notion of arbitrage which arises by excluding liquidation costs from the value process of a portfolio.

Markov chains have experienced a surge of economic interest in the form of behavioral agent-based models that aim at explaining the statistical regularities of financial returns. We review some of the relevant mathematical facts and show how they apply to agent-based herding models, with the...