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Friday, January 26, 2018 at 3:30pm
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.
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.