Quantitative stability of multistage stochastic programs via calm modifications

In this paper, we revisit the quantitative stability of multistage stochastic programs. Different from the single calm modification used in Küchler (2008), we introduce two types of calm modifications which leads to a much simpler proof and tighter upper bound for the difference of optimal values of multistage stochastic programs under different stochastic processes than those of Küchler (2008). In addition, we avoid those restrictive assumptions in Küchler (2008) and the filtration distance in Heitsch et al. (2006). Finally, we illustrate our results with two numerical examples.