Non-standard optimality criteria for stochastic control problems

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., the variance of costs, multiple objectives, robustness with respect to sample path realizations, and sensitivity to long but finite horizon performance as well as long-run average performance.