Predicting Black Swan Events

Jose Blanchet, assistant professor in the Department of Industrial Engineering and Operations Research, has been awarded an NSF CAREER grant that will support research to provide new tools for risk assessment. "Events such as environmental or natural disasters, major market crashes, pension and insurance breakdowns and terrorist attacks are rare but consequential events," says Blanchet. "I hope to develop new and efficient computational tools for risk assessment of rare events that exhibit features such as heavy-tails, complex dependence and incorporation of combinatorial objects."

 

"Efficient evaluation of rare-event probabilities can provide decision makers with key quantitative policy assessment metrics and insights," he says. Examples include assessing ruin probabilities for purposes of sizing the capital reserve of insurance and financial companies and computing the probability that a target is able to evade a set of detectors as well as its conditional most-likely location.

 

NSF's CAREER Program is their most prestigious award for junior faculty. Blanchet's proposal, Efficient Monte Carlo Methods in Engineering and Science: From Coarse Analysis to Refined Estimators, will receive $400,000 in funding.

 

Blanchet will develop a framework that exploits asymptotic analysis, expressed at a coarse scale, to systematically generate efficient rare-event simulation algorithms for complex stochastic systems, which must necessarily be implemented at a fine scale. He will study five types of environments that exhibit stylized features that have not been well studied in rare-event simulation. They are: 1) stochastic recursions with heavy-tails, which are used to model insurance risk and reservoir processes; 2) heavy-tailed queues, which arise in database and networking applications; 3) counting problems and inference for combinatorial structures, which arise in sociology and biology; 4) location of objects immersed in a random medium, with a particular emphasis on military applications to find targets that have eluded detection for a long period of time, and 5) random fields, which arise in oceanography, environmental studies and medical imaging.

 

"My strategy consists in connecting large deviations analysis with algorithmic design of efficient simulation estimators," says Blanchet. "One key tool that I will employ in the design and performance analysis of these algorithms is a systematic use of Lyapunov bounds for Markov chains, combined with parametric families of importance sampling distributions."