16-AUG-2025
We formulate a Huggett-Moll mean field game in which agents’ labor productivity follows a Kou double-exponential jump-diffusion, capturing asymmetric income shocks: sudden collapses and rare windfalls superimposed on geometric Brownian motion. Working in log-productivity space $x = \log z$, the multiplicative jump structure becomes additive, and both the Hamilton-Jacobi-Bellman and Fokker-Planck partial integro-differential equations admit a complete reduction to coupled PDE systems via auxiliary first-order equations derived from the exponential jump kernel. General equilibrium is closed by a Cobb-Douglas production sector, with aggregate capital $K[m] = \iint a \, m(a,x) \, da \, dx$ determining wages and returns endogenously. We state the MFG fixed-point problem, derive the auxiliary PDE systems explicitly, and document a Method of Lines numerical algorithm combining upwind finite differences in wealth with centred fourth-order stencils in log-productivity and a stiff implicit integrator.
