Year: 2026
Type: article
Abstract: . We consider a two-sided singular stochastic control problem with a risk-sensitive ergodic criterion. In particular, we consider a stochastic system whose uncontrolled dynamics are modeled by a linear diffusion. The control that can be applied to the system is modeled by an additive finite variation process. The objective of the control problem is to minimize a risk-sensitive long-term average criterion that penalizes deviations of the controlled process from a given interval, as well as the expenditure of control effort. The stochastic control problem has been partly motivated by the problem faced by a central bank that wishes to control the exchange rate between its domestic currency and a foreign currency so that this fluctuates within a suitable target zone. We derive the complete solution to the problem under general assumptions by deriving a [Formula: see text] solution to its HJB equation. To this end, we use the solutions to a suitable family of Sturm–Liouville eigenvalue problems.
DOI: 10.1137/24m166557x
Authors: Justin Gwee, Mihail Zervos
Institution: London School of Economics and Political Science
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W4414592192
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