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.

中文翻译：

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具有受控跳跃扩散动力学的平均场博弈：存在结果和非流动性银行间市场模型

我们研究了一系列平均场博弈，其状态变量演变为多元跳跃扩散过程。跳跃分量由具有时间依赖强度函数的泊松过程驱动。所有系数，即漂移、波动性和跳跃大小，都受到控制。在相当一般的条件下，我们在平均场博弈的宽松版本中建立解的存在性，并给出最佳策略实际上是马尔可夫的条件，因此扩展到[30]中建立的先前结果的跳跃扩散设置。证明依赖于放松控制和鞅问题的概念。最后，为了补充抽象的存在结果，我们研究了一个简单的非流动性银行间市场模型，