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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Benazzoli, Chiara¹  Campi, Luciano^2,3  Di Persio, Luca⁴ 

[1] Univ Trento, Dept Math, Trento, Italy

[2] London Sch Econ, Dept Stat, London, England

[3] Univ Milan, Dept Math, Milan, Italy

[4] Univ Verona, Dept Comp Sci, Verona, Italy

关键词: Mean field games;    Jump measures;    Controlled martingale problem;    Relaxed controls;    Martingale measure;    Illiquid interbank market model;   

DOI  :  10.1016/j.spa.2020.07.004

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free