Adv. Math. Econ. Volume 4, pp.25-39 (2002)

Dynamic programming with upper semi-continuous stochastic aggregator

Hiroyuki Ozaki
Faculty of Economics, Tohoku University, Kawauchi, Aoba-ku, Sendai 980-8576, Japan

Ozaki and Streufert (1996) develop dynamic programming techniques which are suitably adapted to the recursive objective function which is not necessarily time-separable nor state-separable. To derive their results, they assume that the stochastic aggregator, which generalizes the expectation operator, need be upper quasi-continuous. This paper proposes a new assump-tion on the stochastic aggregator, which we call upper semi-continuity. This is strictly weaker than the upper quasi-continuity. As a main result of this paper, we show that in an important class of problems called the negative dynamic programming, Ozaki and Streufert's result still holds even if we replace the assumption of upper quasi-continuity by the weaker assumption of upper semi-continuity.

Stochastic aggregator, upper semi-continuity, negative dynamic programmlng