Refereed journal article or data article (A1)

Expected Supremum Representation of the Value of a Singular Stochastic Control Problem

List of Authors: Luis H. R. Alvarez E., Pekka Matomäki

Publisher: Society for Industrial and Applied Mathematics

Publication year: 2017

Journal: SIAM Journal on Control and Optimization

Journal acronym: SICON

Volume number: 55

Issue number: 6

Number of pages: 20

ISSN: 0363-0129

eISSN: 1095-7138




We delineate general conditions under which the value of a frequently applied class of singular stochastic control problems of linear diffusions can be represented in a linearized form as an expected supremum of a representing function of the uncontrolled diffusion at an independent exponential random date.
We identify the representing function explicitly in terms of known factors from a Volterra integral equation of the first kind by setting the value accrued from following a standard local time type reflection policy equal to the expected value of the representing function at the running supremum of the underlying. We also illustrate our findings numerically in two explicitly solvable parameterized models subject to different boundary behavior.

Last updated on 2021-24-06 at 09:01