A General Verification Result for Stochastic Impulse Control Problems

SIAM Journal on Control and Optimization, Vol. 55, No. 2, pp. 627-649, 2017

Posted: 3 Jul 2016 Last revised: 2 Sep 2019

See all articles by Christoph Belak

Christoph Belak

Technische Universität Berlin (TU Berlin) - Fakultat II - Mathematik und Naturwissenschaften

Sören Christensen

Gothenburg University

Frank Thomas Seifried

University of Trier

Date Written: December 12, 2016

Abstract

This paper establishes existence of optimal controls for a general stochastic impulse control problem. For this, the value function is characterized as the pointwise minimum of a set of superharmonic functions, as the unique continuous viscosity solution of the quasi-variational inequalities, and as the limit of a sequence of iterated optimal stopping problems. A combination of these characterizations is used to construct optimal controls without relying on any regularity of the value function beyond continuity. Our approach is based on the stochastic Perron method and the assumption that the associated QVIs satisfy a comparison principle.

Keywords: Impulse Control, Stochastic Perron, Superharmonic Functions, Optimal Controls

Suggested Citation

Belak, Christoph and Christensen, Sören and Seifried, Frank Thomas, A General Verification Result for Stochastic Impulse Control Problems (December 12, 2016). SIAM Journal on Control and Optimization, Vol. 55, No. 2, pp. 627-649, 2017, Available at SSRN: https://ssrn.com/abstract=2803068 or http://dx.doi.org/10.2139/ssrn.2803068

Christoph Belak (Contact Author)

Technische Universität Berlin (TU Berlin) - Fakultat II - Mathematik und Naturwissenschaften ( email )

Institut fur Mathematik, Sekr. MA 7-1
Strasse des 17. Juni 136
Berlin, 10623
Germany

Sören Christensen

Gothenburg University ( email )

Göteborg, 41296
Sweden

Frank Thomas Seifried

University of Trier ( email )

Department IV - Mathematics
Universitätsring 19
Trier, 54296
Germany

HOME PAGE: http://sites.google.com/site/seifriedfinance/

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