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

Chiara Benazzoli, Luciano Campi and Luca Di Persio

Stochastic Processes and their Applications, 2020, vol. 130, issue 11, 6927-6964

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 Lacker (2015). 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.

Keywords: Mean field games; Jump measures; Controlled martingale problem; Relaxed controls; Martingale measure; Illiquid interbank market model (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.spa.2020.07.004

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