Constrained optimality for controlled switching diffusions with an application to stock purchasing

Xianggang Lu

Quantitative Finance, 2019, vol. 19, issue 12, 2069-2085

Abstract: This work studies the optimal control of switching diffusions with single constraint. The underlying criterion consists of an expected discounted reward function to be maximized and a discounted cost function as the constraint. Firstly, to solve this constrained problem, the original constrained problem should be converted to the unconstrained one, by introducing the Lagrange multiplier. Then it has been shown that the value function to the unconstrained problem is the unique viscosity solution to the optimality equation, also known as the Hamilton–Jacobi–Bellman equation. A verification theorem is also obtained under suitable conditions. Then, the relationship between the optimality results of the original problem and that of the unconstrained problem can be established, by finding the appropriate Lagrange multiplier. Finally, the optimality results obtained have been applied to characterize the stock purchasing problem. Which is formulated as a constrained optimal purchasing (or control) problem, on behalf of the vendee. The purpose is to investigate optimal purchase strategies and give quantitative reference information for stock purchase. Based on the specific model, a two loop approximation scheme is provided to approximate the optimal value function and the optimal control.

Date: 2019
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://hdl.handle.net/10.1080/14697688.2019.1614210 (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:taf:quantf:v:19:y:2019:i:12:p:2069-2085

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/RQUF20

DOI: 10.1080/14697688.2019.1614210

Access Statistics for this article

Quantitative Finance is currently edited by Michael Dempster and Jim Gatheral

More articles in Quantitative Finance from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().