TY - JOUR
T1 - An optimal sequential procedure for determining the drift of a Brownian motion among three values
AU - Buonaguidi, Bruno
PY - 2023
Y1 - 2023
N2 - We consider a one-dimensional Brownian motion, having a random and unobservable drift which can take one of three known values. Assuming that we monitor the position of the process in real time, the problem is to determine as soon as possible and with minimal probabilities of the wrong terminal decisions, which value the drift has taken. We derive the exact solution to the problem in the Bayesian formulation, under any prior probability distribution on the three values that the drift can assume, when the cost of observation is linear. Remarkably, the optimal stopping boundaries of the present problem are non-monotone.
AB - We consider a one-dimensional Brownian motion, having a random and unobservable drift which can take one of three known values. Assuming that we monitor the position of the process in real time, the problem is to determine as soon as possible and with minimal probabilities of the wrong terminal decisions, which value the drift has taken. We derive the exact solution to the problem in the Bayesian formulation, under any prior probability distribution on the three values that the drift can assume, when the cost of observation is linear. Remarkably, the optimal stopping boundaries of the present problem are non-monotone.
KW - Bayesian formulation
KW - Brownian motion
KW - Free-boundary problem
KW - Non-monotone boundary
KW - Optimal stopping
KW - Sequential analysis
KW - Bayesian formulation
KW - Brownian motion
KW - Free-boundary problem
KW - Non-monotone boundary
KW - Optimal stopping
KW - Sequential analysis
UR - http://hdl.handle.net/10807/228213
U2 - 10.1016/j.spa.2023.02.001
DO - 10.1016/j.spa.2023.02.001
M3 - Article
SN - 0304-4149
VL - 159
SP - 320
EP - 349
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
ER -