The Optimal Stopping Problem Based On A Partially Observable Stochastic Process

We study the optimal stopping problem based on a partially observable stochastic process that can be estimated through the Kalman-Bucy scheme. The reward function in the optimal stopping problem is a mixed function that is the summation of a termi-nal continuous gain function and an integral form of a function including immediate consumption and investment at any time over a random interval. We find the transfor-mation relationship between the optimal stopping problem with incomplete data and the corresponding one with complete data. Based on this relationship, we obtain the convergence of the two corresponding optimal expected rewards when the small per-turbation parameters of the observable process tend to zero.