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...

Ideal economics? A “non-ideal” economics approach has been proposed, which considers the possibility of arrangement infringements. It gives promises for both solving fundamental problems of economic theory and creation of new directions and fields of research. The approach application in...

The definition of arrangement infringement has been given. Several characteristics of hurricanes as large-scale events and objectives for the first stages of insurance data analysis have been sketched out. Scale hypotheses, insurance and investment problems have been formulated.

In this paper we deal with a utility maximization problem at finite horizon on a continuous-time market with conical (and time varying) constraints (particularly suited to model a currency market with proportional transaction costs). In particular, we extend the results in Campi and Owen (2011)...

A man is a key subject of economics and economic theory. “A man is irrational” - this opinion can be made from Allais paradox, risk aversion and other well-known fundamental problems. For a long time, this opinion was a barrier to proper solution of these problems and the development of the...