Robust Sensitivity Analysis for Stochastic Systems

We study a worst-case approach to measure the sensitivity to model misspecification in the performance analysis of stochastic systems. The situation of interest is when only minimal parametric information is available on the form of the true model. Under this setting, we post optimization programs that compute the worst-case performance measures, subject to constraints on the amount of model misspecification measured by Kullback-Leibler divergence. Our main contribution is the development of infinitesimal approximations for these programs, resulting in asymptotic expansions of their optimal values as the divergence shrinks to zero. The coefficients of these expansions can be computed via simulation, and are mathematically derived from the representation of the worst-case models as changes of measure that satisfy a well-defined class of functional fixed-point equations.