Coherent Risk-Adjusted Decisions Over Time: a Bilevel Programming Approach.

摘要

We developed a formal theory of time consistency of multistage systems of stochastic optimization models, analyzing and relating various relevant notions of time consistency. We proved that using multilevel optimization constraints to enforce time consistency results in NP-hard models, even in the simplest cases. However, we also found that a standard MIP solver could solve relatively small but realistic instances of such formulations in minutes. We developed and tested two techniques for approximating a time-inconsistent risk-averse objective function with a time-consistent one. We also investigated rolling-horizon applications of coherent risk measures and risk-averse control of Markov systems. We characterized the sets of optimal solutions to such risk-averse control problems, developing and testing multiple solution methods. We also examined risk-averse transient Markov models. Finally, we developed specialized risk measures for stochastic process control. By considering only random sequences that can actually occur in the controlled system, we were able to derive a much more refined structure than for general risk measures.