Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
The relaxed stochastic maximum principle in singular optimal control of diffusions with controlled diffusion coefficient
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
(English)Manuscript (Other academic)
Keyword [en]
Singular control, Maximum principle, Adjoint equations, Relaxed control, Martingale measures
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-8007OAI: oai:DiVA.org:kth-8007DiVA: diva2:13212
Note
QC 20101102Available from: 2008-02-20 Created: 2008-02-20 Last updated: 2010-11-02Bibliographically approved
In thesis
1. Necessary Optimality Conditions for Two Stochastic Control Problems
Open this publication in new window or tab >>Necessary Optimality Conditions for Two Stochastic Control Problems
2008 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

This thesis consists of two papers concerning necessary conditions in stochastic control problems. In the first paper, we study the problem of controlling a linear stochastic differential equation (SDE) where the coefficients are random and not necessarily bounded. We consider relaxed control processes, i.e. the control is defined as a process taking values in the space of probability measures on the control set. The main motivation is a bond portfolio optimization problem. The relaxed control processes are then interpreted as the portfolio weights corresponding to different maturity times of the bonds. We establish existence of an optimal control and necessary conditions for optimality in the form of a maximum principle, extended to include the family of relaxed controls.

In the second paper we consider the so-called singular control problem where the control consists of two components, one absolutely continuous and one singular. The absolutely continuous part of the control is allowed to enter both the drift and diffusion coefficient. The absolutely continuous part is relaxed in the classical way, i.e. the generator of the corresponding martingale problem is integrated with respect to a probability measure, guaranteeing the existence of an optimal control. This is shown to correspond to an SDE driven by a continuous orthogonal martingale measure. A maximum principle which describes necessary conditions for optimal relaxed singular control is derived.

Place, publisher, year, edition, pages
Stockholm: KTH, 2008. vii p.
Series
Trita-MAT, ISSN 1401-2286 ; 2008-MS-01
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:kth:diva-4643 (URN)978-91-7178-887-0 (ISBN)
Presentation
2008-03-11, Sal E2, Lindstedtsv. 3, Stockholm, 15:15
Opponent
Supervisors
Note
QC 20101102Available from: 2008-02-20 Created: 2008-02-20 Last updated: 2010-11-02Bibliographically approved

Open Access in DiVA

No full text

Search in DiVA

By author/editor
Andersson, Daniel
By organisation
Mathematics (Dept.)
Probability Theory and Statistics

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 81 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf