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This article is cited in 1 scientific paper (total in 1 paper)
Optimal stopping, randomized stopping, and singular control with general information flow
N. Agrama, S. Haademb, B. Øksendalb, F. Proskeb a Department of Mathematics, Linnaeus University, Växjö, Sweden
b Department of Mathematics, University of Oslo, Oslo, Norway
Abstract:
The purpose of this paper is twofold.
First, we extend the well-known relation between optimal stopping and randomized stopping of a given stochastic process to a situation where the available information flow is a filtration with no a priori assumed relation to the filtration of the process. We call these problems optimal stopping and randomized stopping with general information.
Second, following an idea of N. V. Krylov [Controlled Diffusion Processes,
Springer-Verlag, 2009],
we introduce a special singular stochastic control problem with
general information and show that this is also equivalent to the partial
information optimal stopping and randomized stopping problems. Then we show
that the solution of this singular control problem can be expressed in terms
of partial information variational inequalities.
Keywords:
optimal stopping, optimal control, singular control, general information flow.
Received: 27.04.2021 Accepted: 06.07.2021
Citation:
N. Agram, S. Haadem, B. Øksendal, F. Proske, “Optimal stopping, randomized stopping, and singular control with general information flow”, Teor. Veroyatnost. i Primenen., 66:4 (2021), 760–773; Theory Probab. Appl., 66:4 (2022), 601–612
Linking options:
https://www.mathnet.ru/eng/tvp5514https://doi.org/10.4213/tvp5514 https://www.mathnet.ru/eng/tvp/v66/i4/p760
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Abstract page: | 164 | Full-text PDF : | 26 | References: | 17 | First page: | 12 |
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