In this thesis we deal with different topics in financial mathematics, that are all related to market imperfections and to the fundamental technique of utility maximization. The work consists of three parts. In the first one, which is based on two papers, we consider the problem of optimal...

In this article, we characterize efficient portfolios, i.e. portfolios which are optimal for at least one rational agent, in a very general financial market model with proportional transaction costs. In our setting, transaction costs may be random, time-dependent, have jumps and the preferences...

In finite dimensional economies, it was proven by Werner [Werner, J., 1987. Arbitrage and the existence of competitive equilibrium. Econometrica 55, 1403–1418.], that if there exists a no-arbitrage price (equivalently, under standard assumptions on agents' utilities, if aggregate demand exists...