A cross-entropy method optimal stopping problems

There are frequent situations when observations are recorded consecutively over a period of time, for an example, daily values of currency exchange rates. Sequential observations appear one by one, so data are analysed as they are collected without fixing the sample size in advance. Further sampling may be terminated according to a pre-defined stopping rule. There are situations where we need to make decisions considering the observations which are already having while future observations are not known yet. Sequential data analysis has a variety of applications in a wide range of fields including industrial quality control, econometrics, analysis of financial systems among many others. In this thesis, we develop several versions of a Cross-Entropy method to find an approximate optimal stopping rule. Here we have considered cases of both independent and dependent observations. We have carried out a simulation study., which has shown the accuracy of the proposed algorithm.