Optimization under rare events: scaling laws for linear chance-constrained programs
Seminar in Insurance and Economics
SPEAKER: Bert Zwart (CWI Amsterdam & Eindhoven University of Technology).
TITLE: Optimization under rare events: scaling laws for linear chance-constrained programs.
ABSTRACT: We consider a class of chance-constrained programs in which profit needs to be maximized while enforcing that a given adverse event remains rare. Using techniques from large deviations and extreme-value theory, we show how the optimal value scales as the prescribed bound on the violation probability becomes small and how convex programs emerge in the limit. We also use our results to show that the popular Conditional Value at Risk (CVaR) approximation is asymptotically optimal under light-tail assumptions, but is sub-optimal in a heavy-tailed setting. Then, we apply point process techniques and random set theory to study the suboptimality gap in the Monte Carlo-based scenario approach. Time permitting, I will also touch upon the related ongoing work on the problem of determining energy reserves on the Scandinavian grid, where the goal is to prevent a blackout at minimal cost.