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 thesis we explore two recent topics in behavioral finance, namely portfolio optimization by non-expected utility insiders and existence of equilibria in financial markets populated by heterogeneous agents. Firstly, we review a number of theories which have been used to model behavioral...

We prove a general version of the super-replication theorem, which applies to Kabanov’s model of foreign exchange markets under proportional transaction costs. The market is described by a matrix-valued càdlàg bid-ask process $$(\Pi_t)_{t\in [0,T]}$$ evolving in continuous time. We propose a...

We present an optimal investment theorem for a currency exchange model with random and possibly discontinuous proportional transaction costs. The investor’s preferences are represented by a multivariate utility function, allowing for simultaneous consumption of any prescribed selection of the...