Cooperation, Mean Reversion, and Systemic Risk in Interacting Diffusions

Summary

The document analyzes a mean-field model of interacting diffusion processes, where each component has its own stabilizing force in a bistable potential and is also influenced by the system’s empirical mean. Three features shape the dynamics: intrinsic stabilization, external random perturbations, and cooperation. Cooperation is represented as the rate at which each component reverts toward the system mean. The analysis uses large-deviation theory for diffusions coupled through that mean.

In a specified parameter regime, increasing cooperation tends to make individual agents more stable while increasing aggregate systemic risk. This distinction highlights how stabilizing behavior at the component level can have a different effect on the system as a whole. The result depends on the model’s parameter regime and assumptions; the excerpt does not provide calibration to market data, parameter values, or a direct method for forecasting financial crises. It offers a theoretical lens for systemic risk rather than an empirical trading signal.

Key ideas

• The model combines individual bistable stabilization, random perturbations, and interaction through the empirical mean.
• Cooperation is modeled as the rate of mean reversion toward the system average.
• Large-deviation theory is used to study systemic behavior in interacting diffusions.
• In a specified regime, stronger cooperation can stabilize individuals while raising system-wide risk.
• The result is theoretical and depends on the model’s parameter assumptions.

Tags

# Large deviations for a mean field model of systemic risk


# Large deviations for a mean field model of systemic risk









We consider a system of diffusion processes that interact through their empirical mean and have a stabilizing force acting on each of them, corresponding to a bistable potential. There are three parameters that characterize the system: the strength of the intrinsic stabilization, the strength of the external random perturbations, and the degree of cooperation or interaction between them. The latter is the rate of mean reversion of each component to the empirical mean of the system. We interpret this model in the context of systemic risk and analyze in detail the effect of cooperation between the components, that is, the rate of mean reversion. We show that in a certain regime of parameters increasing cooperation tends to increase the stability of the individual agents but it also increases the overall or systemic risk. We use the theory of large deviations of diffusions interacting through their mean field.

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