City Research Online

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

Brunovsky, P., Černý, A. & Winkler, M. (2013). A Singular Differential Equation Stemming from an Optimal Control Problem in Financial Economics. Applied Mathematics & Optimization, 68(2), pp. 255-274. doi: 10.1007/s00245-013-9205-5

Abstract

We consider the ordinary differential equation

x2u′′=axu′+bu−c(u′−1)2,x∈(0,x0),

with

a∈R,b∈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 0=∞ which is such that 0≤u(x)≤x for all x>0, and that this solution is strictly increasing and concave.

Publication Type: Article
Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s00245-013-9205-5
Publisher Keywords: Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, MATHEMATICS, APPLIED, Singular, ODE, Initial value problem, Supersolution, Subsolution, Nonuniqueness
Subjects: H Social Sciences > HB Economic Theory
Q Science > QA Mathematics
Departments: Bayes Business School > Actuarial Science & Insurance
Related URLs:
SWORD Depositor:
[thumbnail of 1209.5027v2.pdf]
Preview
PDF - Accepted Version
Download (242kB) | Preview

Export

Add to AnyAdd to TwitterAdd to FacebookAdd to LinkedinAdd to PinterestAdd to Email

Downloads

Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login