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.
no code implementations • 7 Jul 2022 • Paolo Guasoni, Yu-Jui Huang
Federal student loans are fixed-rate debt contracts with three main special features: (i) borrowers can use income-driven schemes to make payments proportional to their income above subsistence, (ii) after several years of good standing, the remaining balance is forgiven but taxed as ordinary income, and (iii) accrued interest is simple, i. e., not capitalized.
