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

Paolo Guasoni; Kasper Larsen; Giovanni Leoni

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arXiv · 2402.07185

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

Paolo Guasoni·Kasper Larsen·Giovanni Leoni

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Abstract

For constants $\gamma \in (0,1)$ and $A\in (1,\infty)$, we prove existence and uniqueness of a solution to the singular and path-dependent Riccati-type ODE \begin{align*} \begin{cases} h'(y) = \frac{1+\gamma}{y}\big( \gamma - h(y)\big)+h(y)\frac{\gamma + \big((A-\gamma)e^{\int_y^1 \frac{1-h(q)}{1-q}dq}-A\big)h(y)}{1-y},\quad y\in(0,1), h(0) = \gamma, \quad h(1) = 1. \end{cases} \end{align*} 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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Paolo Guasoni, Kasper Larsen, Giovanni Leoni. 2024-02-11. Existence of an equilibrium with limited stock market participation and power utilities. https://arxiv.org/abs/2402.07185

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