CAM Colloquium: Jaakko Lehtomaa (Mathematics, Cornell University) - On heavy-tailed phenomena and the principle of a single big jump

Friday, January 26, 2018 at 3:30pm

Frank H. T. Rhodes Hall, 655

Abstract:
Heavy-tailed distributions have offered an active field of research in insurance mathematics, queuing theory and operations research for decades. This talk concentrates on phenomena that can be encountered in heavy-tailed models. Special emphasis is put on the so-called principle of a single big jump. It means that the most likely way for a sum of i.i.d. variables to be large is that one of the summands itself is very large. We discuss what properties cause the phenomenon of a single big jump.

It turns out that eventual log-convexity or log-concavity of densities is the key ingredient in determining if the principle of a single big jump occurs. In general, well-behaved densities are typically log-convex with heavy tails and log-concave with light ones. We discuss a benchmark and a visual tool for distinguishing between the two cases. The study supplements modern non-parametric density estimation methods where log-concavity plays a main role, as well as heavy-tailed diagnostics such as the mean excess plot.

Bio: 
Lehtomaa received his Ph.D. in 2016 from University of Helsinki. After a postdoctoral study period in Professor Soren Asmussen's group at University of Aarhus, he joined Professor Sid Resnick's group at Cornell University as a postdoctoral researcher. Lehtomaa's research interests have concentrated around the topic of heavy-tailed modeling in insurance and finance. His interests have gradually shifted towards applied problems with real data.

Event Type

Exhibit, Lecture

Departments

College of Engineering, Mathematics, Center for Applied Mathematics

Tags

math, center for applied math, cam, College of Engineering, mathematics, center for applied mathematics

Website

http://cam.cornell.edu

Speaker

Jaakko Lehtomaa, Postdoctoral Researcher

Speaker Affiliation

Department of Mathematics, Cornell University

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