Bayesian sequential least-squares estimation for the drift of a Wiener process

01/16/2019
by   Erik Ekström, et al.
0

Given a Wiener process with unknown and unobservable drift, we seek to estimate this drift as effectively but also as quickly as possible, in the presence of a quadratic penalty for the estimation error and of a linearly growing cost for the observation duration. In a Bayesian framework, this question reduces to choosing judiciously a stopping time for an appropriate diffusion process in natural scale; we provide structural properties of the solution for the corresponding problem of optimal stopping. In particular, regardless of the prior distribution, the continuation region is monotonically shrinking in time. Moreover, conditions on the prior distribution that guarantee a one-sided boundary are provided.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

04/08/2018

A Bayesian sequential test for the drift of a fractional Brownian motion

We consider a fractional Brownian motion with unknown linear drift such ...
02/26/2019

Optimal Stopping of a Brownian Bridge with an Uncertain Pinning Time

We consider the problem of optimally stopping a Brownian bridge with an ...
10/27/2021

A sequential estimation problem with control and discretionary stopping

We show that "full-bang" control is optimal in a problem that combines f...
07/25/2020

A sequential test for the drift of a Brownian motion with a possibility to change a decision

We construct a Bayesian sequential test of two simple hypotheses about t...
11/18/2017

Optimal Stopping for Interval Estimation in Bernoulli Trials

We propose an optimal sequential methodology for obtaining confidence in...
08/03/2019

Sequential tracking of an unobservable two-state Markov process under Brownian noise

We consider an optimal control problem, where a Brownian motion with dri...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.