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Title: Robust classical-impulse stochastic control problems in an infinite horizon
Authors: Pun, Chi Seng
Keywords: Science::Mathematics
Issue Date: 2022
Source: Pun, C. S. (2022). Robust classical-impulse stochastic control problems in an infinite horizon. Mathematical Methods of Operations Research, 96(2), 291-312.
Project: MOE2017-T2-1-044
Journal: Mathematical Methods of Operations Research
Abstract: This paper establishes a general analytical framework for classical and impulse stochastic control problems in the presence of model uncertainty. We consider a set of dominated models, which are induced by the measures equivalent to that of a reference model. The state process under the reference model is a multidimensional Markov process with multidimensional Brownian motion, controlled by continuous and impulse control variates. We propose quasi-variational inequalities (QVI) associated with the value function of the control problem and prove a verification theorem for the solution to the QVI. With the relative entropy constraints and piecewise linear intervention penalty, we show that the QVI can be degenerated to the non-robust case and it can be solved via the solution to a free boundary problem. To illustrate the tractability of the proposed framework, we apply it to a linear-quadratic setting, which covers a broad class of problems including robust mean-reverting inventory controls.
ISSN: 1432-2994
DOI: 10.1007/s00186-022-00795-9
Schools: School of Physical and Mathematical Sciences 
Rights: © 2022 The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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