YRD : Young Researchers Day | September 23, 2022

09:00 – 09:05 : Opening

09:05 – 09:50 : Pierre Devolder & Oussama Belhouari
"Multi-step valuation methods for hybrid life insurance products in a stochastic interest rate framework"

Abstract
In a complete financial market, financial products are valued with the risk- neutral measure and these products are completely hedgeable. In life insurance, the approach is different as the valuation is based on an insurance premium principle which includes a safety loading. The insurer reduces the risk by pooling a vast number of independent contracts. In our framework, we suggest valuations of a class of products that are dependent on both mortality and finance risk, namely hybrid life products. The aim of this paper is to generalize different valuation operators suggested in the literature into a stochastic interest rate framework. We illustrate our methods with a classical application, namely a Pure Endowment with profit. Several numerical results are presented, and an extensive sensitivity analysis is included.

09:50 – 10:20 : Ensiyeh Nezakati
"Distributed estimation of Covariate-adjusted Gaussian graphical models"

Abstract
With the development of technology, the size of the datasets grows at a high rate, such that in certain situations it is not possible to store all needed datasets in the memory of one single machine. Moreover, in recent frameworks, like federated learning, due to privacy concerns, it may be impossible to collect datasets from different resources on one single central machine. As such, the dataset is partitioned onto a cluster of parallel machines. Distributed statistical approaches, also known as ‘divide and conquer’ approaches, have drawn a lot of attention in the last decade and have been developed for various statistical problems. Moreover, inverse covariance matrix estimation plays an important role in statistical and machine learning framework, especially in the framework of Gaussian graphical modeling. Most current methods for inverse covariance matrix estimation assume that the random vector has zero or constant mean. However, in many real applications, like genomic data analysis, it is often important to adjust for covariate effects on the mean of the random vector to obtain more precise estimates. Our purpose is to propose new, unbalanced distributed estimators for both the mean structure and the inverse covariance matrix for covariate-adjusted Gaussian graphical models. These estimators aggregate all local parallel estimators into the final ones by maximizing the pseudo log-likelihood function which comes from the asymptotic distribution of K debiased estimators. Asymptotic behavior and statistical guarantees of these estimators are provided when the number of parameters, covariates and machines all grow with the sample size. A simulation study and a real data example are used to assess the performance of these estimators.

10:20 – 10:50 : Coffee break 

10:50 – 11:20 : Aigerim Zhuman
"Combination of Control Variates and Adaptive Importance Sampling"

Abstract
Adaptive importance sampling and control variates are two widely used variance reduction techniques associated with Monte Carlo integration. The adaptive importance sampling method is based on updating the sampling policy, the sequence of distributions used to generate the particles. The method of control variates consists of projecting the integrand on the linear space spanned by a vector of auxiliary functions with known expectations, called control variates. We propose to incorporate control variates into the adaptive importance sampling procedure in order to improve the accuracy of Monte Carlo integration. The obtained estimate, called the AISCV estimate, arises as the weighted least squares estimate for the intercept in a multiple linear regression model where control variates are used as explanatory variables. Moreover, we introduce a quadrature rule with adapted quadrature weights which do not depend on the integrand. The latter property is computationally advantageous in case of multiple integrands. Our main result states a concentration inequality for the normalized AISCV integration error. The performance of the AISCV estimate is illustrated on synthetic examples and real-world data for Bayesian linear regression.

11:20 – 11:50 : Stephan Lhaut
"Uniform concentration bounds for frequencies of rare events"             

Abstract
Statistical Learning Theory stressed the problem of finite sample guarantees and motivated the study of concentration inequalities between a risk functional (unknown) to be minimized and its empirical version on the sample (known), holding uniformly over a class of functions of finite complexity. Many results are available, but in a multivariate extreme value context, these bounds may not capture well the rare nature of the encountered events and hence overestimate the difference between the true and empirical risk. In a binary classification framework, we propose specific inequalities designed to handle such events. The derived bounds are explicit, enabling numerical comparisons.

11:50 – 12:20 : Anas Mourahib
"Sparse multivariate Generalized Pareto distributions"

Abstract
Consider a random vector representing risk factors and suppose that we are interested in extreme scenarios. The Peaks Over Thresholds method is widely used in extreme value theory. It uses the fact that asymptotically, exceedances over a high threshold can be modelled using a multivariate Generalized Pareto distribution. In the literature, statistical practice of this method has been discussed only when all risks are large simultaneously. This condition is not realistic for example when some of the risks are nearly independent. To address this point, we construct a parametric model that allows some risks to be large without the other ones. We also compute the density of this model and estimate the parameters using Maximum Likelihood.  

12 :20 – 12:30 : Closing