Data-driven satisficing measure and ranking
This work addresses risk management challenges in domains like finance or operations research, but it appears incremental as it builds on existing risk measure concepts.
The authors tackled the problem of real-time risk assessment and ranking for random outcomes without known probability distributions by proposing a computational framework based on satisficing measure, deriving convergence rates and regret bounds for offline and online optimization cases, and illustrating the relationship between risk ranking accuracy and sample size or iterations.
We propose an computational framework for real-time risk assessment and prioritizing for random outcomes without prior information on probability distributions. The basic model is built based on satisficing measure (SM) which yields a single index for risk comparison. Since SM is a dual representation for a family of risk measures, we consider problems constrained by general convex risk measures and specifically by Conditional value-at-risk. Starting from offline optimization, we apply sample average approximation technique and argue the convergence rate and validation of optimal solutions. In online stochastic optimization case, we develop primal-dual stochastic approximation algorithms respectively for general risk constrained problems, and derive their regret bounds. For both offline and online cases, we illustrate the relationship between risk ranking accuracy with sample size (or iterations).