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On a mixed singular/switching control problem with multiple regimes

Part of: Control systems Hamilton-Jacobi theories, including dynamic programming Stochastic systems and control

Published online by Cambridge University Press:  22 August 2022

Mark Kelbert  and
Harold A. Moreno-Franco Open the ORCID record for Harold A. Moreno-Franco [Opens in a new window]
Mark Kelbert*
Affiliation:
HSE University
Harold A. Moreno-Franco*
Affiliation:
HSE University
*
*Postal address: National Research University Higher School of Economics (HSE), Faculty of Economics, Department of Statistics and Data Analysis, Moscow, Russian Federation.
*Postal address: National Research University Higher School of Economics (HSE), Faculty of Economics, Department of Statistics and Data Analysis, Moscow, Russian Federation.
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Abstract

This paper studies a mixed singular/switching stochastic control problem for a multidimensional diffusion with multiple regimes on a bounded domain. Using probabilistic partial differential equation and penalization techniques, we show that the value function associated with this problem agrees with the solution to a Hamilton–Jacobi–Bellman equation. In this way, we see that the regularity of the value function is $ \textrm{C}^{0,1}\cap \textrm{W}^{2,\infty}_{\textrm{loc}}$ .

Keywords

Singular/switching stochastic control problemHamilton–Jacobi–Bellman equationsnonlinear partial differential system

MSC classification

Primary: 49L99: None of the above, but in this section
Secondary: 93E20: Optimal stochastic control 93C30: Systems governed by functional relations other than differential equations (such as hybrid and switching systems)
Type
Original Article
Information
Advances in Applied Probability , Volume 54 , Issue 3 , September 2022 , pp. 743 - 782
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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