7 papers
Large and Moderate Deviations for Conservative Tail-Index Estimation
Martijn Gösgens, Bart P. G. van Parys, Bert Zwart
To design systems that are protected against events much rarer than the observational record, extreme-value methods are needed to extrapolate distribution tails. Tail-index estimat…
Decision-Centric Large Deviations for Data-Driven Capital Buffers in Ruin Models
Yf Henkes, Bart P. G. van Parys, Bert Zwart
We consider an insurance risk model with a random walk structure in which the underlying probability law is unknown. A decision maker observes a statistic computed from h…
Large deviations for subgraphs in inhomogeneous random graphs
Riccardo Michielan, Clara Stegehuis, Bert Zwart
Inhomogeneous random graphs are fundamental models for real-world networks, where prescribed degrees are imposed as soft constraints. A common assumption in such models is that the…
Sample Path Large Deviations for Multivariate Heavy-Tailed Hawkes Processes and Related Lévy Processes
Jose Blanchet, Roger J. A. Laeven, Xingyu Wang +1
In this paper, we develop sample path large deviations for multivariate Hawkes processes with heavy-tailed mutual excitation rates. Our results address a broad class of rare events…
Tail Asymptotics of Cluster Sizes in Multivariate Heavy-Tailed Hawkes Processes
Jose Blanchet, Roger J. A. Laeven, Xingyu Wang +1
We examine a distributional fixed-point equation related to a multi-type branching process that is key in the cluster sizes analysis of multivariate heavy-tailed Hawkes processes.…
Optimization under rare events: scaling laws for linear chance-constrained programs
Jose Blanchet, Joost Jorritsma, Bert Zwart
We consider a class of chance-constrained programs in which profit needs to be maximized while enforcing that a given adverse event remains rare. Using techniques from large deviat…
Large deviations of the giant component in scale-free inhomogeneous random graphs
Joost Jorritsma, Bert Zwart
We study large deviations of the size of the largest connected component in a general class of inhomogeneous random graphs with iid weights, parametrized so that the degree distrib…