Monte Carlo Methods for Adaptive Disorder Problems

We develop a Monte Carlo method to solve continuous-time adaptive disorder problems. An unobserved signal X undergoes a disorder at an unknown time to a new unknown level. The controller’s aim is to detect and identify this disorder as quickly as possible by sequentially monitoring a given observation process Y . We adopt a Bayesian setup that translates the problem into a two-step procedure of (i) stochastic filtering followed by (ii) an optimal stopping objective. We consider joint Wiener and Poisson observation processesY and a variety of Bayes risk criteria. Due to the general setting, the state of our model is the full infinite-dimensional posterior distribution of X . Our computational procedure is based on combining sequential Monte Carlo filtering procedures with the regression Monte Carlo method for high-dimensional optimal stopping problems. Results are illustrated with several numerical examples.