We study the connection between the martingale and free-boundary approaches in sequential detection problems for the drift of a Brownian motion, under the assumption of exponential penalty for the delay. By means of the solution of a suitable free-boundary problem, we show that the reward process can be decomposed into the product between a gain function of the boundary point and a positive martingale inside the continuation region.
- Modeling and Simulation
- Statistics and Probability
- free-boundary problem
- martingale approach of Beibel
- optimal stopping
- sequential detection and disorder problems