{"paper":{"title":"A Singular Differential Equation Stemming from an Optimal Control Problem in Financial Economics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.OC","authors_text":"Ale\\v{s} \\v{C}ern\\'y, Michael Winkler, Pavol Brunovsk\\'y","submitted_at":"2012-09-22T22:47:54Z","abstract_excerpt":"We consider the ordinary differential equation $x^2 u'' = axu'+bu-c(u'-1)^2, x\\in (0,x_0)$, with $a\\in\\mathbb{R}, b\\in\\mathbb{R}$, $c>0$ and the singular initial condition $u(0)=0$, which in financial economics describes optimal disposal of an asset in a market with liquidity effects. It is shown in the paper that if $a+b < 0$ then no solutions exist, whereas if $a+b\\ge0$ then there are infinitely many solutions with indistinguishable asymptotics near 0. Moreover, it is proved that in the latter case there is precisely one solution $u$ corresponding to the choice $x_0=\\infty$ which is such tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5027","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}