  In this paper, we address linear-quadratic-Gaussian (LQG) risk-sensitive mean
field games (MFGs) with common noise. In this framework agents are exposed to a
common noise and aim to minimize an exponential cost functional that reflects
their risk sensitivity. We leverage the convex analysis method to derive the
optimal strategies of agents in the limit as the number of agents goes to
infinity. These strategies yield a Nash equilibrium for the limiting model. The
model is then applied to interbank markets, focusing on optimizing lending and
borrowing activities to assess systemic and individual bank risks when reserves
drop below a critical threshold. We employ Fokker-Planck equations and the
first hitting time method to formulate the overall probability of a bank or
market default. We observe that the risk-averse behavior of agents reduces the
probability of individual defaults and systemic risk, enhancing the resilience
of the financial system. Adopting a similar approach based on stochastic
Fokker-Planck equations, we further expand our analysis to investigate the
conditional probabilities of individual default under specific trajectories of
the common market shock.
