A sequential estimation problem with control and discretionary stopping
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We show that "full-bang" control is optimal in a problem that combines features of (i) sequential least-squares estimation with Bayesian updating, for a random quantity observed in a bath of white noise; (ii) bounded control of the rate at which observations are received, with a superquadratic cost per unit time; and (iii) "fast" discretionary stopping. We develop also the optimal filtering and stopping rules in this context.
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