Geodesic
Optimal stopping, randomized stopping, and singular control with general information flow
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 4, pp. 760-773

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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. 
@article{TVP_2021_66_4_a7,
     author = {N. Agram and S. Haadem and B. {\O}ksendal and F. Proske},
     title = {Optimal stopping, randomized stopping, and singular control with general information flow},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {760--773},
     publisher = {mathdoc},
     volume = {66},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_4_a7/}
}
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N. Agram; S. Haadem; B. Øksendal; F. Proske. Optimal stopping, randomized stopping, and singular control with general information flow. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 4, pp. 760-773. http://geodesic.mathdoc.fr/item/TVP_2021_66_4_a7/