Toward Scalable Risk Analysis for Stochastic Systems Using Extreme Value Theory

We aim to analyze the behaviour of a finite-time stochastic system, whose model is not available, in context more rare and harmful outcomes. Standard estimators are effective making predictions about such outcomes due their rarity. Instead, we use Extreme Value Theory (EVT), theory long-term normalized maxima random variables. quantify risk using upper-semideviation P(Y)≔(max{Y-μ,0}) an integrable variable Y with mean μ≔E(Y). P(Y) risk-aware part common mean-upper-semideviation functional φλ(Y)≔μ+λρ(Y) λ0,1. To assess outcomes, propose EVT-based estimator for ρ(Y) given fraction worst cases. show that our enjoys closed-form representation terms popular conditional value-at-risk functional. In experiments, illustrate extrapolation power small number i.i.d. samples (<50). Our approach useful estimating systems when models inaccessible data collection expensive. The numerical complexity does grow size state space.