Dynamic network models with applications to finance

This thesis provides new contributions to the field of network models, in two directions. On one hand, we study statistical models of static networks, in particular by contributing to the problem of community detection when link direction is taken into account, thus identifying what are the macroscopic structures of interest for the problem and the conditions for detectability [Wilinski et al., 2019]. Then, we introduce novel statistical models of dynamic networks which are able to capture simultaneously latent dynamics for node-specific characteristics together with link-specific persistence patterns. While the latent dynamics drives the evolution of the network topologies, such as the node degree, i.e. the number of incident links to the node, or the community structure, i.e. how nodes connect each other in forming groups, link persistence preserves the past structure of the network. Within this context, the contribution of the thesis is twofold, both theoretical and empirical [Mazzarisi et al., 2019a, Barucca et al., 2018]. We develop novel methodologies to disentangle the two linkage mechanisms in order to learn correctly both latent variables and static parameters of the models. And we consider also applications to financial data to reveal genuine patterns of persistence, which reflects the role both nodes and links have in the process of network formation and evolution. On the other hand, with a focus on the systemic risk of financial systems, we present a theoretical study of the expectation feedback mechanism which governs the dynamics of a financial network, thus determining its dynamical stability [Mazzarisi et al., 2019b]. Any financial system is an expectation feedback system: the current decisions of financial agents depend on what they expect will occur in the future. Agents\u2019 decisions affect the price dynamics in illiquid markets. Then, when expectations are formed by using models of past observations, the price dynamics itself feeds back on agents\u2019 expectations. This is in effect a feedback dynamics. Interestingly, the process of expectation formation by agents and the price dynamics act on different time scales. In our modeling, it is slow for the agents\u2019 expectations and fast for the price dynamics. Moreover, the agents\u2019 decisions, given the expectations formed on the basis of the random price dynamics, is to some extent deterministic, because they represent the optimal portfolio choice in a heavily regulated market. This separation of time scales is crucial and we are able to characterize analytically the feedback dynamics in the asymptotic limit of one time scale infinitely larger than the other one. Hence, we contribute to the research field of systemic risk with the first analytical proof (to the best of our knowledge) of how expectation feedbacks in relation to the estimation of investments\u2019 risk and dependencies determine the dynamical instability of a financial system. In line with the two research directions, the thesis is divided in two parts. [...