Quadratic minimization with portfolio and terminal wealth constraints

Andrew Heunis ()

Annals of Finance, 2015, vol. 11, issue 2, 243-282

Abstract: We address a problem of stochastic optimal control drawn from the area of mathematical finance. The goal is to minimize the expected value of a general quadratic loss function of the wealth at close of trade when there is a specified convex constraint on the portfolio over the trading interval, together with a specified almost-sure lower-bound on the wealth at close of trade. We use a variational approach of Rockafellar which leads naturally to an appropriate vector space of dual variables, a dual functional on the space of dual variables such that the dual problem of maximizing the dual functional is guaranteed to have a solution (i.e. a Lagrange multiplier) when a simple and natural Slater condition holds for the terminal wealth constraint, and obtain necessary and sufficient conditions for optimality of a candidate wealth process. The dual variables are pairs, each comprising an Itô process paired with a member of the adjoint of the space of essentially bounded random variables measurable with respect to the event $$\sigma $$ σ -algebra at close of trade. The necessary and sufficient conditions are used to construct an optimal portfolio in terms of the Lagrange multiplier. The dual problem simplifies to maximization of a concave function over the real line when the portfolio is unconstrained but the terminal wealth constraint is maintained. Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Portfolio optimization; Stochastic control; Conjugate duality; Constraints; Lagrange multiplier; Slater condition; C61; C65; G11 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10436-014-0254-9 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:kap:annfin:v:11:y:2015:i:2:p:243-282

Ordering information: This journal article can be ordered from
http://www.springer.com/finance/journal/10436/PS2

DOI: 10.1007/s10436-014-0254-9

Access Statistics for this article

Annals of Finance is currently edited by Anne Villamil

More articles in Annals of Finance from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().