Abstract: Two-stage stochastic optimization models are widely used in modern operational problems such as investment portfolios and transportation management. In two-stage stochastic optimization, the sample average approximation method is commonly used. The existing research generally assumes that the sample is generated by the real distribution, but the actual situation of the sample may be contaminated, then we need to know whether the optimal value of the two-stage stochastic optimization problem is reliable. This paper investigates the quantitative statistical robustness of the sample average approximation of the optimal value for full random two-stage stochastic optimization problems where the second-stage objective function is a linear function, a piecewise linear function, or a class of convex functions. When the objective function is a linear function, based on the stability analysis of the full random stochastic optimization problem, the quantitative statistical robustness of the sample average approximation to the optimal value is studied. When the objective function is a piecewise linear function, the uniform Lipschitz continuity of the optimal value function in the second stage is derived by proving a uniform bound on feasible dual solutions, thus obtaining the quantitative statistical robustness results of the full random two-stage stochastic optimization problem. The method is extended to a class of full random two-stage stochastic optimization problems where the objective function is a convex function, and the quantitative statistical robustness of the sample average approximation to the optimum of the problem is analyzed.

Key words: full random, statistical robustness, two-stage stochastic optimization, sample average approximation