Non-Standard Optimality Criteria for Stochastic Control Problems

Abstract

In this paper, we survey several recent developments on non- standard optimality criteria for controlled Markov process models of stochastic control problems. Commonly, the criteria employed for optimal decision and control are either the discounted cost (DC) or the long-run average cost (AC). We present results on several other criteria that, as opposed to the AC or DC, take into account, e.g., a) the variance of costs; b) multiple objectives; c) robustness with respect to sample path realizations; d) sensitivity to long but finite horizon performance as well as long-run average performance.