Quantitative Stability For Scenario-Based Stochastic Programs

General quantitative stability results for stochastic programs are formulated in terms of probability metrics, specified to scenario-based stochastic programs and applied to a bond portfolio management problem. AMS classification: 90C15, 90C31, 60K30, 90C08 Key words : Probability metrics, stochastic programs, stability wrt. probability measure, random recourse, discrete distributions, application 1 INTRODUCTION Stability and sensitivity studies for stochastic programs have been motivated by an incomplete information about the probability measure through which the stochastic program is formulated and also by the efforts in designing various discretization and approximation schemes needed in connection with the development and evaluation of algorithms. The solved real life stochastic programs are very complex; in numerical procedures, one uses their specific structure and is interested in robust solutions: Small changes in the input (in our case mainly perturbations of the probabili..