Existence of an equilibrium with limited stock-market participation and power utilities

For constants γ ∈ (0,1) and A∈ (1,∞), we prove existence of a solution to the singular and path-dependent Riccati-type ODE {align*} {cases} h'(y) = 1+γ/y( γ - h(y))+h(y){γ + ((A-γ)e∫_y^1 1-h(q)/1-qdq-A)h(y)}{1-y}, y∈(0,1), \\ h(0) = γ, h(1) = 1. {cases} {align*} As an application, we use the ODE solution to prove existence of an equilibrium with homogenous power traders in the limited participation setting of Basak and Cuoco (1998).