Faculty of Actuarial Science & Insurance with Dr Yahia Salhi (ISFA University Claude Bernard)

Abstract

We consider the minimax quickest detection problem of an unobservable time of proportional change in the intensity of a doubly-stochastic Poisson process. We seek a stopping rule that minimizes the robust Lorden criterion, formulated in terms of the number of events until detection, both for the worst-case delay and the false alarm constraint. This problem, introduced by Page [Biometrika 41 (1954) 100–115], has received more attention in the continuous path framework (for Wiener processes) than for point processes, where optimality results only concern the Bayesian framework [In Advances in Finance and Stochastics (2002) 295–312, Springer, Berlin]. In this work, we prove the CUSUM optimality conjectured but not solved for the Poisson case of the CUSUM strategy in the general setting of the stochastic intensity framework. Applications to the surveillance of biometric assumptions in life insurance is discussed using real world datasets.

Biography

Yahia Salhi holds a PhD in applied mathematics from the University of Lyon, a MSc in actuarial science and finance from ISFA, and an engineering diploma from the Ecole des Mines. He is assitant professor at ISFA Graduate School of Actuarial Studies and associate researcher at the BNP Paribas Cardif's "Data Analytics & Models in Insurance's Chair" (DAMI). Yahia's main research interests include detection of abrupt changes, longevity and mortality modelling, pricing and management as well as surrender risk modelling and mathematical aspects of impairment of financial assets under IFRS regulations. Yahia lectures on actuarial and financial mathematics in various universities and actuarial programs: Saint-Joseph University (Lebanon), Université Internationale de Rabat (Morocco), Université Cheikh Anta Diop (Sénégal), Université Paris Dauphine (Tunisia) and at ISFA (France) among others.