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Expected Supremum Representation of the Value of a Singular Stochastic Control Problem
TLDR
The problem of representing the value of singular stochastic control problems of linear diffusions as expected suprema by setting the value accrued from following a standard reflection policy equal with the expected value of a unknown function at the running supremum of the underlying is considered.Abstract:
We consider the problem of representing the value of singular stochastic control problems of linear diffusions as expected suprema. Setting the value accrued from following a standard reflection policy equal with the expected value of a unknown function at the running supremum of the underlying is shown to result into a functional equation from which the unknown function can be explicitly derived. We also consider the stopping problem associated with the considered singular stochastic control problem and present a similar representation as an expected supremum in terms of characteristics of the control problem.read more
Citations
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Connections between Optimal Stopping and Singular Stochastic Control I. Monotone Follower Problems
TL;DR: In this article, the stochastic control problem of tracking a Brownian motion by a non-decreasing process (Monotone Follower) is related to the question of optimal stopping.
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