Mean Field Games with Kou Jump-Diffusion Productivity

We study a mean field game formulation of the Huggett–Moll heterogeneous-agent economy under Kou jump-diffusion productivity shocks. The stationary equilibrium is characterised by a coupled system of a PIDE (Hamilton–Jacobi–Bellman with jumps) and a Kolmogorov forward equation. We derive an auxiliary PDE reduction that eliminates the non-local integral term and admit a purely local PDE system amenable to Howard iteration.

Abstract

Standard Huggett–Moll economies assume Brownian motion productivity. We replace this with a double-exponential (Kou) jump-diffusion, capturing the asymmetric tail behaviour documented in micro-level panel data. The PIDE structure introduces a non-local operator that we resolve via Wiener–Hopf factorisation, reducing the system to a cascade of local PDEs. Stationary distributions are computed via finite-difference upwind schemes on an adaptive grid.