Numerical methods for optimal stopping using linear and non-linear programming

Computational methods for optimal stopping problems are presented. The first method to be described is based on a linear programming approach to exit time problems of Markov processes and is applicable whenever the objective function is a unimodal function of a threshold parameter which specifies a stopping time. The second method, using linear and non-linear programming techniques, is a modification of a general linear programming approach to optimal stopping problems recently proposed by S. Rohl. Both methods are illustrated by solving Shiryaev's quickest detection problem for Brownian motion.