Stopping problems for random fields with partially nested information

This paper formulates a general optimal stopping problem for random fields with a partially ordered parameter set and with a partially ordered information structure in the sense of Ho and Chu [1]. It is possible in this framework of partially ordered parameters to formulate naturally a wide variety of stopping problems which are difficult or impossible to formulate in the conventional one-parameter framework. The dynamic programming solution of the one-parameter stopping problem extends to the more general case of partially ordered parameters. The resulting dynamic program is backward recursive with respect to the partial order, and this recursive property enables one to use the full structure of the partially ordered parameter set to calculate the solution to the stopping problem in an efficient manner.