A1 Refereed original research article in a scientific journal
Expected Supremum Representation of the Value of a Singular Stochastic Control Problem
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: 55
Issue: 6
First page : 3908
Last page: 3927
Number of pages: 20
ISSN: 0363-0129
eISSN: 1095-7138
DOI: https://doi.org/10.1137/15M1034957
Web address : https://doi.org/10.1137/15M1034957
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.