ARC 2025 - Étienne Marceau

Multivariate Bernoulli Distributions with Actuarial Applications

Moderator: Tom Salisbury, Professor Emeritus, York University

Multivariate Bernoulli distributions are essential in the modeling of binary data in a wide variety of contexts, such as actuarial science, quantitative risk management, machine learning, natural language processing, and bioinformatics. In this talk, I will present recent results on two topics related to multivariate Bernoulli distributions.

In the first part of my talk, I will consider tree-structured Ising models, a class of undirected graphical models for Bernoulli random vectors. We introduce a stochastic representation of the components of the Bernoulli random vectors such that the marginal distributions remain fixed. That representation has many advantages: to find the Pearson's correlation coefficient for any pairs of components of Bernoulli random vectors; to design an efficient sampling algorithm; and to investigate properties of the tree-structured multivariate Bernoulli distributions. We also derive an analytic expression for the joint probability generating function of the Bernoulli random vector. The latter is used to build efficient computation methods for the sum of the components of the Bernoulli random vector.

In the second part, I will discuss negative dependence for Bernoulli random vectors. We will provide the essential tools of negative dependence and extremal negative dependence in a common language and the framework of multivariate Bernoulli distributions. We will characterize sigma-countermonotonicity and study the strongly Rayleigh property within this class. We will illustrate those notions using the class of conditional Bernoulli distributions.

To conclude, I will present examples with actuarial applications of the results from the two topics.

Étienne's Bio

Étienne Marceau is a Full Professor at the School of Actuarial Science at Université Laval. He has been Distinguished Visiting Scholar at UNSW (2019), Visiting Professor at Université Lyon III (2005-2024), and Adjunct Professor at McGill University (2015-2021). His research interests focus on topics which are the intersections of actuarial science, applied probability, and applied statistics, such as dependence modeling and actuarial modeling. He has taught courses on actuarial modeling, risk theory, life contingencies, survival models, and financial mathematics. Strongly believing in HQP training, he has supervised 9 PhD, 31 MSc, and 35 BSc students. He has published more than 60 scientific articles, mostly with HQP, and he is the author of “Modélisation et évaluation quantitative des risques en actuariat” (Springer 2014). He holds the NSERC Discovery Grant and he co-PI on two NSERC CRD grants. He is the co-chair of the ACTRISK laboratory at Université Laval, of the CIMMUL, and a member of the editorial board of Insurance: Mathematics and Economics. He has been chair of CRM-Quantact. He has also been involved with the Society of Actuaries (SOA), as a Faculty for the Course 7 and a Faculty Advisor on the evaluation committee of the CAE of the SOA. He is a member of CIMMUL, CRDM , and CIRCERB. He served as an external research and development advisor, notably for Aon Hewitt, the Quebec Pension Plan and Industrial Alliance.