A sequential estimation problem with control and discretionary stopping

2021/10/27 by Ekström, Erik, Karatzas, Ioannis · 2 citations
#62L12 #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2110.14366

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.

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