skip to main content

SciTech ConnectSciTech Connect

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

We consider the ordinary differential equation x{sup 2} u'' = axu'+bu-c(u'-1){sup 2}, x Element-Of (0,x{sub 0}), with a Element-Of R, b Element-Of 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 continuous solutions exist, whereas if a+b>0 then there are infinitely many continuous 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{sub 0}={infinity} which is such that 0{<=}u(x){<=}x for all x>0, and that this solution is strictly increasing and concave.
Authors:
 [1] ;  [2] ;  [3]
  1. Comenius University Bratislava, Department of Applied Mathematics and Statistics (Slovakia)
  2. City University London, Cass Business School (United Kingdom)
  3. Universitaet Paderborn, Institut fuer Mathematik (Germany)
Publication Date:
OSTI Identifier:
22210462
Resource Type:
Journal Article
Resource Relation:
Journal Name: Applied Mathematics and Optimization; Journal Volume: 68; Journal Issue: 2; Other Information: Copyright (c) 2013 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; AUGMENTATION; DIFFERENTIAL EQUATIONS; IMAGES; OPTIMAL CONTROL