Large deviations for Minkowski sums of heavy-tailed random compact sets

Mathematical Finance/Financial Engineering Seminar
Friday, February 11, 2011 - 15:05
1 hour (actually 50 minutes)
Skiles 002
School of Operations Research and Information Engineering, Cornell University

Hosted by Christian Houdre and Liang Peng

We prove large deviation results for Minkowski sums S_n of iid random compact sets, both convex and non-convex, where we assume that the summands have a regularly varying distribution and either finite or infinite expectation. The results confirm the heavy-tailed large deviation heuristics: "large'' values of the sum are essentially due to the "largest'' summand.