https://macropaperwarehouse.com/authors/jordan-roulleau-pasdeloup/Jordan Roulleau-PasdeloupHugo -- gohugo.ioen-ushttps://macropaperwarehouse.com/papers/explicit-consumption-functions-with-borrowing-constraints-a-continuous-time-approach/https://macropaperwarehouse.com/papers/explicit-consumption-functions-with-borrowing-constraints-a-continuous-time-approach/<p><strong>Research question.</strong> The paper asks whether an explicit, global, closed-form solution exists for the consumption function in the standard income fluctuation problem with a borrowing constraint and constant income, a problem that has resisted closed-form solution since at least Schechtman (1976). All prior continuous-time work (Park 2006, Holm 2018, Fischer 2024) produced only <em>implicit</em> expressions; Achdou et al. (2022) produced explicit expressions valid only locally, near zero assets or as assets diverge to infinity, and only for r &gt; 0.</p>