preprint

Inserted: 25 dec 2024

Year: 2024

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_y¹ \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).