A sequential estimation problem with control and discretionary stopping

<p style='text-indent:20px;'>We show that “full-bang” control is optimal in a problem which combines features of (i) sequential least-squares <i>estimation</i> with Bayesian updating, for random quantity observed bath white noise; (ii) bounded <i>control</i> the rate at observations are received, superquadratic cost per unit time; and (iii) “fast” discretionary <i>stopping</i>. We develop also filtering stopping rules this context.</p>