Using particle system methodologies we study the propagation of financial distress in a network of firms facing credit risk. We investigate the phenomenon of a credit crisis and quantify the losses that a bank may suffer in a large credit portfolio. Applying a large deviation principle we compute the limiting distributions of the system and determine the time evolution of the credit quality indicators of the firms, deriving moreover the dynamics of a global financial health indicator. We finally describe a suitable version of the “Central Limit Theorem” useful to study large portfolio losses. Simulation results are provided as well as applications to portfolio loss distribution analysis

We study the impact of contagion in a network of firms facing credit risk. We describe an intensity based model where the homogeneity assumption is broken by introducing a random environment that makes it possible to take into account the idiosyncratic characteristics of the firms. We shall see that our model goes behind the identification of groups of firms that can be considered basically exchangeable. Despite this heterogeneity assumption our model has the advantage of being totally tractable. The aim is to quantify the losses that a bank may suffer in a large credit portfolio. Relying on a large deviation principle on the trajectory space of the process, we state a suitable law of large numbers and a central limit theorem useful for studying large portfolio losses. Simulation results are provided as well as applications to portfolio loss distribution analysis.

We analyze the implications of innovation and social interactions on economic growth in a stylized endogenous growth model with heterogeneous research firms. A large number of research firms decide whether to innovate or not, by taking into account what competitors (i.e., other firms) do. This is due to the fact that their profits partly depend on an externality related to the share of firms which actively engage in research activities. Such a share of innovative firms also determines the evolution of technology in the macroeconomy, which ultimately drives economic growth. We show that when the externality effect is strong enough multiple BGP equilibria may exist. In such a framework, the economy may face a low growth trap suggesting that it may end up in a situation of slow long-run growth; however, such an outcome may be fully solved by government intervention. We also show that whenever multiple BGP exist, they are metastable meaning that the economy may cyclically fluctuate between the low and high BGP as a result of shocks affecting the individual behavior of research firms. Forthcoming in Economic Theory AbstractWe analyze the implications of innovation and social interactions on economic growth in a stylized endogenous growth model with heterogenous research firms. A large number of research firms decide whether to innovate or not, by taking into account what competitors (i.e., other firms) do. This is due to the fact that their profits partly depend on an externality related to the share of firms which actively engage in research activities. Such a share of innovative firms also determines the evolution of technology in the macroeconomy, which ultimately drives economic growth. We show that when the externality effect is strong enough multiple BGP equilibria may exist. In such a framework, the economy may face a low growth trap suggesting that it may end up in a situation of slow long run growth; however, such an outcome may be fully solved by government intervention. We also show that whenever multiple BGP exist, they are metastable meaning that the economy may cyclically fluctuate between the low and high BGP as a result of shocks affecting the individual behavior of research firms.

This paper studies opinion dynamics for a set of heterogeneous populations of individuals pursuing two conflicting goals: to seek consensus and to be coherent with their initial opinions. The multi-population game under investigation is characterized by (i) rational agents who behave strategically, teractions. The main contribution of this paper is to encompass all of these aspects under the unified framework of mean-field game theory.We show that, assuming initial Gaussian density functions and affine control policies, the Fokker-Planck-Kolmogorov equation preserves Gaussianity over time. This fact is then used to explicitly derive expressions for the optimal control strategies when the players are myopic. We then explore consensus formation depending on the stubbornness of the involved populations: we identify conditions that lead to some elementary patterns, such as consensus, polarization or plurality of opinions.Finally, under the baseline example of the presence of a stubborn population and a most gregarious one, we study the behavior of the model with a finite number of players, describing the dynamics of the average opinion, which is now a stochastic process. We also provide numerical simulations to show how the parameters impact the equilibrium formation.

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We propose a discrete-time stochastic dynamics for a system of many interacting agents. At each time step agents aim at maximizing their individual payoff, depending on their action, on the global trend of the system and on a random noise; frictions are also taken into account. The equilibrium of the resulting sequence of games gives rise to a stochastic evolution. In the limit of infinitely many agents, a law of large numbers is obtained; the limit dynamics consist in an implicit dynamical system, possibly multiple valued. For a special\ud model, we determine the phase diagram for the long time behavior of these limit dynamics and we show the existence of a phase, where a locally stable fixed point coexists with a locally stable periodic orbit

We analyze the implications of innovation and social interactions on economic growth in a stylized endogenous growth model with heterogeneous research firms. A large number of research firms decide whether to innovate or not, by taking into account what competitors (i.e., other firms) do. This is due to the fact that their profits partly depend on an externality related to the share of firms which actively engage in research activities. Such a share of innovative firms also determines the evolution of technology in the macroeconomy, which ultimately drives economic growth. We show that when the externality effect is strong enough multiple BGP equilibria may exist. In such a framework, the economy may face a low growth trap suggesting that it may end up in a situation of slow long-run growth; however, such an outcome may be fully solved by government intervention. We also show that whenever multiple BGP exist, they are metastable meaning that the economy may cyclically fluctuate between the low and high BGP as a result of shocks affecting the individual behavior of research firms. Forthcoming in Economic Theory AbstractWe analyze the implications of innovation and social interactions on economic growth in a stylized endogenous growth model with heterogenous research firms. A large number of research firms decide whether to innovate or not, by taking into account what competitors (i.e., other firms) do. This is due to the fact that their profits partly depend on an externality related to the share of firms which actively engage in research activities. Such a share of innovative firms also determines the evolution of technology in the macroeconomy, which ultimately drives economic growth. We show that when the externality effect is strong enough multiple BGP equilibria may exist. In such a framework, the economy may face a low growth trap suggesting that it may end up in a situation of slow long run growth; however, such an outcome may be fully solved by government intervention. We also show that whenever multiple BGP exist, they are metastable meaning that the economy may cyclically fluctuate between the low and high BGP as a result of shocks affecting the individual behavior of research firms.

We provide a simple micro-foundation of the tourism area life cycle hypothesis, based on tourists’ utility maximization. As a result of social interactions among tourists which determine destinations popularity, the market share of visitors which decides to visit a specific destination follows a logistic dynamics, consistent with what predicted by the tourism area life cycle hypothesis. We show that different preference drivers explain the duration of the different tourism area life cycle stages: the net benefit from visiting the destination characterizes the exploration, involvement, and development phases, while social effects associated with destination popularity characterize the phases of consolidation and stagnation Different from previous studies our results hold true independently of whether we focus on the repeating or non-repeating segment of the tourism market. We also provide a calibration of our model to the case of the city of Venice (Italy) showing that it performs well in capturing the evolution of tourism in the historical center of the city over the last 60 years, suggesting that TALC-like dynamics may occur even in the context of cultural and heritage destinations.