A Singular Differential Equation Stemming from an Optimal Control Problem in Financial Economics

Pavol Brunovský, Aleš Černý, Michael Winkler

We consider the ordinary differential equation $x^2{u}^{\prime \prime }=ax{u}^{\prime }+bu-c(u^{\prime }-1{)}^2,x\in (0,x_0)$, with $a\in \mathbb{R},b\in \mathbb{R}$, $c>0$ and the singular initial condition $u(0)=0$…