STABILITY OF A CLASS OF RISK-AVERSE MULTISTAGE STOCHASTIC PROGRAMS AND THEIR DISTRIBUTIONALLY ROBUST COUNTERPARTS

摘要

In this paper, we consider the quantitative stability of a class ofrisk-averse multistage stochastic programs, whose objective functions are de-fined by multi-period pth order lower partial moments (LPM) with given targets,and their distributionally robust counterparts. We first derive the upperbounds of feasible solutions as preliminaries. Then, by employing calm modifi-cations, the quantitative stability results are obtained under a special measurableperturbation of stochastic process, which extend the present results underrisk-neutral cases to risk-averse ones. Moreover, we recast the risk-averse modelby probability measures of stochastic process, and obtain new quantitative stabilityestimations on the basis of proper probability metrics under the generalperturbation of stochastic process. Finally, motivated by the availability ofonly partial information about probability measures, we further consider thedistributionally robust counterpart of our recasting model, and establish thediscrepancy of optimal values with respect to the perturbation of ambiguitysets.