2021/07/29 by Volker Krätschmer, Krätschmer, Volker
Decision Sciences · Engineering · #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Mathematical Programming #Probability (math.PR) #Risk and Portfolio Optimization #Water resources management and optimization
paper · pdf · doi:10.48550/arxiv.2107.13863
openalex publication_date 2021/07/29 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
We investigate statistical properties of the optimal value of the Sample\nAverage Approximation of stochastic programs, continuing the study in\nKr "atschmer (2023). Central Limit Theorem type results are derived for the\noptimal value. As a crucial point the investigations are based on a new type of\nconditions from the theory of empirical processes which do not rely on pathwise\nanalytical properties of the goal functions. In particular, continuity in the\nparameter is not imposed in advance as usual in the literature on the Sample\nAverage Approximation method. It is also shown that the new condition is\nsatisfied if the paths of the goal functions are H "older continuous so that\nthe main results carry over in this case. Moreover, the main results are\napplied to goal functions whose paths are piecewise H "older continuous as e.g.\nin two stage mixed-integer programs. The main results are shown for classical\nrisk neutral stochastic programs, but we also demonstrate how to apply them to\nthe Sample Average Approximation of risk averse stochastic programs. In this\nrespect we consider stochastic programs expressed in terms of absolute\nsemideviations and divergence risk measures.\n