A singular stochastic control problem with direction switching cost

Łukasz Kruk ()
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Łukasz Kruk: Maria Curie-Skłodowska University

Mathematical Methods of Operations Research, 2023, vol. 98, issue 3, No 1, 325-349

Abstract: Abstract We introduce a new class of singular stochastic control problems in which the process controller not only chooses the push intensity, at a price proportional to the displacement caused by his action, but he can also change the allowable control direction, paying a fixed cost for each such switching. Singular control of the one-dimensional Brownian motion with quadratic instantaneous cost function and costly direction switching on the infinite time horizon is analyzed in detail, leading to a closed-form solution. This example is used as an illustration of qualitative differences between the class of problems considered here and classic singular stochastic control.

Keywords: Singular stochastic control; Stochastic switching; Direction switching cost; HJB equations; Brownian motion; Explicit solution; 93E20; 60J65 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00186-023-00839-8

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