Programme YRD 15/02/2019

09h00 : Sophie Mathieu
"Uncertainty Quantification in Sunspot Counts"

09h30 : Nathalie Lucas
"Experience rating in health insurance using a Hidden Markov Model"

10h00 : Oswaldo Gressani
"Bayesian P-splines and Laplace's method for inference in generalized additive models"

10h30 : Coffee break
 
11h00 : Michel Thiel
"Comparison of chemometrics methods for the spectroscopic monitoring of active pharmaceutical ingredients in chemical reactions"

11h30 : Florian Pechon
"Multivariate Claim Frequencies in Motor Insurance using Household Data"

12h00 : Charles-Guy Njike Leunga
"Risk management of interest rate derivatives in presence of interbank risk"
 

Abstracts

Sophie Mathieu
"Uncertainty Quantification in Sunspot Counts"

Abstract :
Sunspots are dark spots appearing in groups on the solar surface as a manifestation of solar magnetism.  While the time series of sunspot counts acts as a benchmark  in a large variety of physical sciences, as of today it lacks proper uncertainty quantification and modeling. This presentaiton details the first comprehensive noise model of the sunspot counts in a multiplicative framework. We estimate the various error terms using  Hurdle models combined with overdispersed distributions. Key results are an estimation of short-term error distribution, and an estimation of long-term drift specific to each observatory.

Nathalie Lucas
"Experience rating in health insurance using a Hidden Markov Model"

Abstract :
The main purpose of the research is to develop i) efficient actuarial models of pricing and reserving and ii) risk classification techniques for health insurance products.
In this regard, credibility theory is applied for experience rating in health insurance products. Health insurance claims are delivered sequentially in time and constitute panel or longitudinal data, inducing serial correlation. We assume a dynamic heterogeneity and hence propose  a Hidden Markov Model, also called state-dependent or dependent mixture model. We show how the maximum likelihood estimators of the parameters of a HMM can be suitably obtained using the EM algorithm and we apply the HMM to model yearly individual health-related costs of a private German insurer.

Oswaldo Gressani
"Bayesian P-splines and Laplace's method for inference in generalized additive models"

Abstract :
Ever since the dawn of statistical science, regression analysis has played a central role in the literature, giving birth to models that grew in profusion to accommodate all sorts of relationships between variables of interest. Generalized additive models (GAMs) are a well-established statistical tool for modeling complex nonlinear relationships between a response belonging to an exponential family and a set of covariates. Recently, an approximate Bayesian approach termed Integrated Nested Laplace Approximations (INLA) has emerged in the literature and has been largely acclaimed for its computational efficiency to obtain posterior marginals in structured additive regression models with a Gaussian latent field. We develop a novel inferential methodology for GAMs characterized by a flexible estimation of smooth functions with Bayesian P-splines and a rapid approximation of joint posterior distributions of latent model variables with Laplace's method. The gradient and Hessian of the hyperparameters are analytically available and a moment-matching technique allows to capture possible asymmetries in the posterior distribution of the penalty vector. The suggested methodology is an extension of the Laplace-P-spline model proposed in which has proved to work well in a particular class of survival models, largely outperforming the computational speed of Markov chain Monte Carlo methods. A simulation study is implemented as a performance measure and the well-known gam function is taken as a competitor.

Michel Thiel
"Comparison of chemometrics methods for the spectroscopic monitoring of active pharmaceutical ingredients in chemical reactions"

Abstract :
The Process Analytical Technology (PAT) initiative promoted by the Food and Drug Administration (FDA) encourages pharmaceutical companies to increase the use of new analytical technologies to perform constant monitoring of the critical quality attributes (CQA) allowing better process understanding and control. 
Matching those PAT requirements, spectroscopic methods in the range of infrared have become widely used to monitor critical process attributes such as the active content. Those methods produce spectral data which are often difficult to interpret due to their multivariate nature. For this reason, the use of chemometric methods is needed to extract the relevant information and understand the chemical mechanisms. 
A set of 11 chemical experiments monitored by mid-infrared spectroscopy (MIR) and ultra-pressure liquid chromatography (UPLC) will be used to apply dimension-reduction methods principal component analysis (PCA), non-negative matrix factorization (NMF) and multivariate curve resolution (MCR). Those methods decompose a matrix of multivariate data, such as in spectroscopy, into scores and loadings matrices representing rows (observations) and columns (variables) into a space of reduced dimensions. Scores can help to follow reaction components over time while loadings can help to detect influencial spectroscopic variables. 
There are two objectives in this presentation. The first one is to compare PCA, NMF and MCR to follow the evolution of the main chemical compounds in the reaction, in term of interpretability and error estimations. Those methods will also be compared in term of methodology. The second objective is to compare the capability of those methods to predict the quantities of the main compounds which will open the way to model chemical reactions.

Florian Pechon
"Multivariate Claim Frequencies in Motor Insurance using Household Data"

Abstract :
Actuarial risk classification studies are typically confined to univariate, policy-based analyses:
individual claim frequencies are modelled for a single guarantee in isolation, without accounting for the interactions between the different coverages bought by the same policyholder. Moreover, independence between the policyholders is generally assumed. However, some events may trigger multiple guarantees at the same time. Moreover, some unobserved but important risk factors may be shared across a household, inducing dependence between policyholders from the same household.
We present some ideas using multivariate credibility theory on how the dependence between the different products can be captured, while also accounting for the dependence between policyholder from the same household. The analysis is performed on a motor insurance portfolio, using the two most common guarantees: Third-Party Liability insurance and Material Damage insurance.
The results show that the dependence between the claim frequencies of the two considered guarantees is strong, even when considering different policyholders living in the same household. The model in turn allows obtaining better predictions of the claim frequencies and possible cross-selling opportunities can be identified.

Charles-Guy Njike Leunga
"Risk management of interest rate derivatives in presence of interbank risk"

Abstract :
The credit crunch in 2007-2008 caused major changes in the interbank market rates making existing interest rate theory inconsistent. Based on the work of Mercurio, we remind one way to reconcile practice and theory by modifying the arbitrage-free condition. In this framework, the simple forward Libor rate is not considered anymore as a risk-free rate and its dynamic is driven by the presence of the credit and liquidity risk within the interbank market. We model the simple forward Libor rate taking into account the new market features through the multiple-curve approach studied by Filipovic and Trolle , and Henrard. In this approach, we model the joint evolution of the default-free rates, assimilated to overnight interest swap rates, and the default times of the interbank market. To deal with the credit risk of this generic counterparty we use the reduced form approach and model the arrival rate of defaults by a self-exciting jump-diffusion process. The diffusion part is structured as a CIR model to insure both the non-negativity and mean-reverting property. Whereas the jump part follows an inhomogeneous Poisson process that allows positive jump when a credit event occurs. We next deduce the dynamic of the simple spot forward Libor rates, and explicitly present the impact of jumps on the Libor dynamic. We finally provide pricing formulae for options on simple forward Libor rates and swap rates.