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arXiv · 1703.01919

Mean field games with controlled jump-diffusion dynamics: Existence results and an illiquid interbank market model

Chiara Benazzoli·Luciano Campi·Luca Di Persio
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Abstract

We study a family of mean field games with a state variable evolving as a multivariate jump diffusion process. The jump component is driven by a Poisson process with a time-dependent intensity function. All coefficients, i.e. drift, volatility and jump size, are controlled. Under fairly general conditions, we establish existence of a solution in a relaxed version of the mean field game and give conditions under which the optimal strategies are in fact Markovian, hence extending to a jump-diffusion setting previous results established in [30]. The proofs rely upon the notions of relaxed controls and martingale problems. Finally, to complement the abstract existence results, we study a simple illiquid inter-bank market model, where the banks can change their reserves only at the jump times of some exogenous Poisson processes with a common constant intensity, and provide some numerical results.

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Chiara Benazzoli, Luciano Campi, Luca Di Persio. 2020-07-11. Mean field games with controlled jump-diffusion dynamics: Existence results and an illiquid interbank market model. https://arxiv.org/abs/1703.01919

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