A1 Refereed original research article in a scientific journal

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




AuthorsLuis H. R. Alvarez E., Pekka Matomäki

PublisherSociety for Industrial and Applied Mathematics

Publication year2017

JournalSIAM Journal on Control and Optimization

Journal acronymSICON

Volume55

Issue6

First page 3908

Last page3927

Number of pages20

ISSN0363-0129

eISSN1095-7138

DOIhttps://doi.org/10.1137/15M1034957

Web address https://doi.org/10.1137/15M1034957


Abstract

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 2024-26-11 at 17:46