Oskar Laverny

Oskar Laverny

Actuary, PhD



Actuary by formation, I focused during my PhD on high dimensional statistics and dependence structure estimations applied to internal modeling in a reinsurance context. I am currently a Post-Doctoral researcher at UCLouvain, in Belgium, under an FNRS grant. I do have a taste for numerical code and open-source software, and most of my work is freely available.


  • High dimensional statistics
  • Dependence modeling
  • Code
  • Actuarial Sciences


  • PhD: Dependence structure and risk agregation in high dimensions., 2019-2022

    ICJ & SCOR

  • Master in Mathematics - Probability, 2018-2019

    ENS Lyon

  • Bachelor, Master and Diploma in Actuarial Sciences, 2015-2018


  • Bachelor in Mathematics, 2012-2015

    University of Straßbourg

Recent Publications

Parametric divisibility of stochastic losses

A probability distribution is n-divisible if its nth convolution root exists. While modeling the dependence structure between several (re)insurance losses by an additive risk factor model, the infinite divisibility, that is the n-divisibility for all interger n, is a very desirable property. Moreover, the capacity to compute the distribution of a piece (i.e., a convolution root) is also desirable. Unfortunately, if many useful distributions are infinitely divisible, computing the distributions of their pieces is usually a challenging task that requires heavy numerical computations. However, in a few selected cases, particularly the Gamma case, the extraction of the distribution of the pieces can be performed fully parametrically, that is with negligible numerical cost and zero error. We show how this neat property of Gamma distributions can be leveraged to approximate the pieces of other distributions, and we provide several illustrations of the resulting algorithms.

Estimation of high dimensional Gamma convolutions through random projection

Multivariate generalized Gamma convolutions are distributions defined by a convolutional semi-parametric structure. Their flexible dependence structures, the marginal possibilities and their useful convolutional expression make them appealing to the practitioner. However, fitting such distributions when the dimension gets high is a challenge. We propose stochastic estimation procedures based on the approximation of a Laguerre integrated square error via (shifted) cumulants approximation, evaluated on random projections of the dataset. Through the analysis of our loss via tools from Grassmannian cubatures, sparse optimization on measures and Wasserstein gradient flows, we show the convergence of the stochastic gradient descent to a proper estimator of the high dimensional distribution. We propose several examples on both low and high-dimensional settings.

Estimation of multivariate generalized gamma convolutions through Laguerre expansions

The generalized gamma convolutions class of distributions appeared in Thorin’s work while looking for the infinite divisibility of the log-Normal and Pareto distributions. Although these distributions have been extensively studied in the univariate case, the multivariate case and the dependence structures that can arise from it have received little interest in the literature. Furthermore, only one projection procedure for the univariate case was recently constructed, and no estimation procedures are available. By expanding the densities of multivariate generalized gamma convolutions into a tensorized Laguerre basis, we bridge the gap and provide performant estimation procedures for both the univariate and multivariate cases. We provide some insights about performance of these procedures, and a convergent series for the density of multivariate gamma convolutions, which is shown to be more stable than Moschopoulos’s and Mathai’s univariate series. We furthermore discuss some examples.

Empirical and non-parametric copula models with the cort R package

The R package cort implements object-oriented classes and methods to estimate, simulate and visualize certain types of non-parametric copulas.

Dependence structure estimation using Copula Recursive Trees

We construct the Copula Recursive Tree (CORT) estimator: a flexible, consistent, piecewise linear estimator of a copula, leveraging the patchwork copula formalization and various piecewise constant density estimators. While the patchwork structure imposes a grid, the CORT estimator is data-driven and constructs the (possibly irregular) grid recursively from the data, minimizing a chosen distance on the copula space. The addition of the copula constraints makes usual denisty estimators unusable, whereas the CORT estimator is only concerned with dependence and guarantees the uniformity of margins. Refinements such as localized dimension reduction and bagging are developed, analyzed, and tested through applications on simulated data.

Recent & Upcoming Talks



Inférence statistique des tests - CM + TD

ENS Lyon

Sep 2021 – Jan 2022
  • 36h integrated lectures (main lecture + tutorials) given to third year students in Economics.
  • Content: From the definition of a probability to mean and variance tests in the Gaussian or asymptotically Gaussian cases, chi-squared tests, with a particular emphasis on Cochran’s proof. Kolomogorov-Smirnov test with a full proof. Maximum Likelyhood estimation and likelyhood-ratio tests.
  • The particularity was that I had the opportunity to create and design the content and the form of lectures myself.

Probabilité, combinatoire et statistiques - TD

University Claude Bernard Lyon 1

Jan 2021 – May 2021
  • 30h tutorials given to third year students in Mathematics.
  • Content: From the definition of a probability to mean and variance tests in the Gaussian or asymptotically Gaussian cases, chi-squared tests. Discrete time markov chains. Numerical applications in R

Statistiques pour l’informatique - TD

University Claude Bernard Lyon 1

Sep 2020 – Jan 2022
  • 30h tutorials given to second year students in Informatics, in Falls 2020 and Falls 2021.
  • Content: From the definition of a probability to mean and variance tests in the Gaussian or asymptotically Gaussian cases, chi-squared tests. Numerical applications in R.

Recent Posts

Estimation and sampling of copulas in Julia with Copulas.jl

Announce I am proud to annonce the publication and the registration of my new Julia package, Copulas.jl. As it’s name suggests, Copulas.jl is a package that implements methods and tools to work with an arround copulas in the Julia programming language.

Automatic latex resume with github action and gitinfo2 watermark

The problematic A latex-written resume is always a nice thing to have: easy to update, practical to integrate .bib bibliographies, and automatic management of the look (you only provide its content).

Using Git and Github for LaTeX writing

The problematic As an academic, I spend my life writing papers. Since these papers are mostly about math or some applications of math, I am an extensive user of latex.



Post-Doctoral Researcher

UCLouvain - ISBA

Oct 2022 – Present Paris & Lyon
FNRS-funded post doc position.


SCOR & Univ Lyon 1

Jun 2019 – Jun 2022 Paris & Lyon
The title of the PhD is “Dependence structures and risk agregations in high dimensions.” The PhD was defended on May, the 30th of 2022.



May 2017 – Sep 2018 Lyon
Non Life reserving of french builder’s insurence in a Solvency II context :

  • Analysis
  • Construction of an USP
  • Redaction of an actuarial thesis on it.