Robust classical-impulse stochastic control problems in an infinite horizon

Chi Seng Pun ()
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Chi Seng Pun: Nanyang Technological University

Mathematical Methods of Operations Research, 2022, vol. 96, issue 2, No 6, 312 pages

Abstract: 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.

Keywords: Stochastic control; Robustness; Mixed classical and impulse controls; Quasi-variational inequalities; Robust inventory controls (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00186-022-00795-9

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