no code implementations • 11 Feb 2024 • Paolo Guasoni, Kasper Larsen, Giovanni Leoni
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.
