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Agram, N.; Haadem, S.; Øksendal, B.; Proske, F.

Optimal stopping, randomized stopping, and singular control with general information flow. (English) Zbl 1480.60103

Theory Probab. Appl. 66, No. 4, 601-612 (2022) and Teor. Veroyatn. Primen. 66, No. 4, 760-773 (2021).
Summary: 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. Translated by A. B. Aries. Berlin: Springer (2009; Zbl 1171.93004)], 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.

MSC:

60G40 Stopping times; optimal stopping problems; gambling theory
93E20 Optimal stochastic control

Keywords:

optimal stopping; optimal control; singular control; general information flow

Citations:

Zbl 1171.93004
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Full Text: DOI arXiv

References:

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