This thesis contains some of the main results obtained during my research activity in these years, in the Statistical Physics sector at SISSA and in the Quantitative Life Sciences sector at ICTP.
Chapter 1 serves as an introduction and is kept brief, because each of the following chapters has a separate introduction containing more details on the different problems that have been considered.
In Chapter 2 several models of wealth dynamics are discussed, with focus on the stationary distributions that they have. In particular, we introduce a stochastic growth model that has a truncated power law distribution as a stationary state, and we give an interpretation for the mechanism generating this cut-off as a manifestation of the shadow banking activity.
Chapter 3 is devoted to the issue of wealth inequality, and in particular to its consequences, when in a system with a power law wealth distribution, economic exchanges are considered. A stylized model of trading dynamics is introduced, in which we show how as inequality increases, the liquid capital concentrates more and more on the wealthiest agents, thereby suppressing the liquidity of the economy.
Finally in Chapter 4, we discuss the issue of complexity and information sensitiveness of financial products. In particular, we introduce a stylized model of binary variables, where the financial transparency can be quantified in bits. We quantify how such information losses create sources of systemic risk, and how they should affect the pricing of financial products.
