Caroline Hillairet: Risk Quantification of Cumulative Losses exhibiting contagion and cross dependencies
Time: Mon 2025-01-27 15.15 - 15.45
Location: 3721 (Lindstedtsvägen 25)
Participating: Caroline Hillairet (Institut Polytechnique de Paris)
Abstract
Risk analysis for credit or actuarial portfolios is usually based on the study of the so-called cumulative loss process
\[L_T = \sum_{i = 1}^{N_T} Y_i, \qquad T \ge 0.\]\((N_t)_{t \ge 0}\) is a counting process that models the arrivals of the claims, as the defaults for a credit portfolio, or the sinistres for an insurance portfolio, while the random variables \((Y_i)_i\) model the claims amounts. We extend the classic Cramer-Lundberg model by allowing contagion and dependency phenomena, as observed in credit risk or cyber risk. This model (called Multivariate Self-Exciting Process with Dependencies) is an extension of the Hawkes process in which the excitation kernel \(\Phi\) is affected by the claims sizes, and thus introducing dependencies between the severity and the frequency components. Using new technics at the crossroad of the so-called Poisson imbedding and Malliavin’s calculus, we develop theoretical results on such processes and present several applications in terms of risk quantification.
Based on joint works with Thomas Peyrat and Anthony R´eveillac