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

2024/02/11 by Guasoni, Paolo, Larsen, Kasper, Leoni, Giovanni · 1 citation
#Analysis of PDEs (math.AP) #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF)

paper · doi:10.48550/arxiv.2402.07185

Abstract

For constants γ∈ (0,1) and A∈ (1,∞), we prove existence and uniqueness of a solution to the singular and path-dependent Riccati-type ODE \begincases h'(y) = (1+γ)/(y)( γ- h(y))+h(y)\fracγ+ ((A-γ)e^{∫_y1 (1-h(q))/(1-q)dq}-A)h(y)1-y, y∈(0,1), h(0) = γ, h(1) = 1. \endcases As an application, we use the ODE solution to prove existence of a Radner equilibrium with homogenous power-utility investors in the limited participation model from Basak and Cuoco (1998).

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• Long-run survival in limited stock market participation models with power utilities

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