A sequential estimation problem with control and discretionary stopping-Reference-Cited by-同舟云学术

A sequential estimation problem with control and discretionary stopping

Published:2022 Issue:3 Volume:7 Page:151
ISSN:2095-9672
Container-title:Probability, Uncertainty and Quantitative Risk
language:
Short-container-title:PUQR

Author:

Ekström Erik¹,Karatzas Ioannis²

Affiliation:

1. Department of Mathematics, Uppsala University, Box 256, 75105 Uppsala, Sweden

2. Departments of Mathematics and Statistics, Columbia University, 2990 Broadway, New York, NY 10027, USA

Abstract

We show that “full-bang” control is optimal in a problem which 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.

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Medicine

Reference24 articles.

1. Bensoussan, A. and Lions, J. L., Applications of Variational Inequalities in Stochastic Control, North-Holland, Amsterdam and New York, 1982.

2. Chung, K. L., A Course in Probability Theory, Second Edition, Probability and Mathematical Statistics: A Series of Monographs and Textbooks, vol. 21. Academic Press, New York, 1974.

3. Dalang, R. C. and Shiryaev, A. N., A quickest detection problem with observation cost, Ann. Appl. Probab., 2015, 25(3): 1475−1512.

4. Davis, M. H. A. and Zervos, M., A problem of singular stochastic control with discretionary stopping, Ann. Appl. Probab., 1994, 4(1): 226−240.

5. Dubins, L. E. and Savage, L. J., How to Gamble if You Must: Inequalities for Stochastic Processes, McGraw-Hill Publishing Co., NY. Re-issued in 2014, edited and updated by W. D. Sudderth and D. Gilat, as a Dover Publication, Mineola, NY, 1965.