Dynamic Programming

This chapter studies the dynamic programming principle when applied to the general stochastic optimization problem of Chap. 1 . Our approach builds on the notion of conditional expectation of a normal integrand, which allows for significant extensions to many better known dynamic programming formulations while greatly simplifying the measurability questions that come up in dynamic programming recursions. More traditional forms of dynamic programming will be obtained as special cases as illustrated by the examples at the end of the chapter.