A sequential estimation problem with control and discretionary stopping
Probability
2022-11-10 v2 Statistics Theory
Statistics Theory
Abstract
We show that "full-bang" control is optimal in a problem that combines features of (i) sequential least-squares {\it estimation} with Bayesian updating, for a random quantity observed in a bath of white noise; (ii) bounded {\it control} of the rate at which observations are received, with a superquadratic cost per unit time; and (iii) "fast" discretionary {\it stopping}. We develop also the optimal filtering and stopping rules in this context.
Cite
@article{arxiv.2110.14366,
title = {A sequential estimation problem with control and discretionary stopping},
author = {Erik Ekström and Ioannis Karatzas},
journal= {arXiv preprint arXiv:2110.14366},
year = {2022}
}