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Current research topics
My research is currently focused on the following themes:
I recently created and developed the R package admix, which allows to estimate the unknown parameters of admixture models, to perform hypothesis tests and to do clustering of unknown component densities. The full implementation of this is available to everyone on my Github webpage, so do not hesitate to contribute and suggest me improvements!
More on this at the following link, with full package documentation available here.
As scientific director of the Research project DIALog (Digital Insurance and Long term risks) with Katrien Antonio, I currently focus on statistical learning and corresponding developments to deal with typical insurance data. In the past, my PhD thesis made me develop many research interests, among which classification issues, generalized linear models and survival analysis. I have been particularly interested in Classification and Regression Trees (CART algorithm), and ensemble methods (e.g. Random Forests).
- Artificial Intelligence and Machine Learning algorithms, with applications to insurance and actuarial sciences,
- Admixture (aka contamination) models and finite mixtures (see my Github webpage),
- Survival analysis and competing risks models,
- Generalized linear models and model selection,
- Self-excited processes (Hawkes process).
Considering Generalized Linear Models was straightforward to make comparisons, as an extension to classical regression techniques which enables to specify some different link functions in order to model various response variables. I personnally used the logistic link to model surrender/lapse behaviours, and compared this method with other classification algorithms in a discriminant analysis perspective.
Concerning Survival Analysis, I performed some studies using the famous proportional hazards model by Cox (1972), but also used other intensity models like Weibull or the Accelerated (respectively Decelerated) Failure Time model. I compared these models to competing risks models, an adequate framework to study endpoints (contract lifetime) in life insurance. A natural extension concerns how to deal with censored/truncated data in nonparametric regression techniques such as regression trees.
I also had to deal with problems like overdispersion and heterogeneity. This made me investigate another framework: Finite Mixture Models, and their dynamic extension known as Regime Switching Models. The aim was to develop new results in terms of model selection in this framework. On one hand, my recent research thus focuses on GLM Markov switching models, as well as self-excited processes since they allow us to integrate dynamic correlation between agents. On the other hand, those matters also appear in nonparametric settings, which explains the focus of my recent theoretical research.
Additional information about the DIALog research project and related research topics can be found here.
Published papers and main talks
I would like to thank again my co-authors for these works together.
...and the following talks (non exhaustive list):
- Published papers:
- X. Milhaud, D. Pommeret, Y. Salhi, P. Vanderkerkhove, Semiparametric two-sample admixture components comparison test: the symmetric case, accepté dans Journal of Statistical Planning and Inference, (2021). Lien HAL ici
- Milhaud, X., Hétérogénéité inobservable, volumétrie limitée et mutualisation, L'Actuariel, 39 (2021).
- O. Lopez, X. Milhaud, Individual reserving and nonparametric estimation of claim amounts subject to large reporting delays, Scandinavian Actuarial Journal, (2020) ; doi:10.1080/03461238.2020.1793218. Link to an old version of the paper
- O. Lopez, X. Milhaud, P.-E. Therond, A tree-based algorithm adapted to microlevel reserving and long development claims, ASTIN Bulletin, (2019) Volume 49 issue 3, pp.741-762 ; doi:10.1017/asb.2019.12. Link to an old version of the paper
- X. Milhaud, V. Poncelet, C. Saillard, Operational choices for risk aggregation in insurance: PSDization and SCR sensitivity, Risks, (2018) Volume 6 issue 36, pp.1-22 ; doi:10.3390/risks6020036. Link to an old version of the paper
- X. Milhaud, C. Dutang, Lapse tables for lapse risk management in insurance: a competing risk approach, European Actuarial Journal, (2018) Volume 8 issue 1, pp.97-126 ; doi:10.1007/s13385-018-0165-7. Link to an old version of the paper
- O. Lopez, X. Milhaud, P. Therond, Tree-based censored regression with applications in insurance, Electronic Journal of Statistics, (2016) Volume 10 issue 2, pp.2685-2716. Link to an old version of the paper
- F. Barsotti, X. Milhaud, Y. Salhi, Lapse risk in life insurance: correlation and contagion effects among policyholders' behaviors, Insurance: Mathematics and Economics, (2016) Volume 71, pp.317-331. Link to an old version of the paper
- Milhaud X., Exogenous and endogenous risk factors management to predict surrender behaviours, ASTIN Bulletin, (2013) Volume 43 issue 3, pp.373-398, DOI: 10.1017/asb.2013.2. Link to the paper
- Loisel S., Milhaud X., From deterministic to stochastic surrender risk models: impact of correlation crises on economic capital, European Journal of Operational Research (EJOR), (2011) Volume 214 issue 2, pp.348-357. Link to an old version of the paper
- Milhaud X., Maume-Deschamps V. et Loisel S., Surrender triggers in Life Insurance: what main features affect the surrender behavior in a classical economic context?, Bulletin Francais d'Actuariat (BFA), (2011) n.22, pp.5-48. Link to an old version of the paper
- Milhaud X., Gonon M-P. et Loisel S., Les comportements de rachat en Assurance Vie en régime de croisière et en période de crise, Risques, (2010) Volume 83, pp.76-81 (Link to an old (french!) version of the paper).
- Submitted, in revision process, or working papers:
- X. Milhaud, D. Pommeret, Y. Salhi, P. Vanderkerkhove, Shape constraint free two-sample contamination model testing.Lien HAL vers l'article
- P. Chatelain, X. Milhaud, Regression and data quality through individualized credibility index.
- X. Milhaud, D. Pommeret, Y. Salhi, P. Vanderkerkhove, K-sample tests and clustering.
- X. Milhaud, admix: an R package for estimation, testing and clustering in admixtures.
- C. Genest, X. Milhaud, P. Vanderkerkhove, Independence test in multivariate admixture models.
- P. Chatelain, X. Milhaud, Integrating data quality into GLM for fair insurance pricing.
- X. Milhaud, P. Vanderkerkhove, Concordance test for paired samples.
- C. Genest, X. Milhaud, Aggregating correlated loss triangles, a credibility approach.
- X. Milhaud, Excess-of-loss reinsurance and credibility premiums.
- Microlevel reserving in long-development business lines, OICA-WAKA Conference (Online), 05/2020;
- Truncation and reporting delays in reserving, 7th SMIF Conference, Maresias (Brazil), 03/2020;
- Microlevel reserving with tree-based regression in presence of censoring and truncation, Invited talk at CASS Business School, London (UK), 01/2020;
- A tree-based algorithm adapted to claims with long development, IME Conference, Munich Germany), 07/2019;
- Surrender tables for ALM in insurance, with competing risks, EAJ Conference, KU Leuven (Belgium), 09/2018;
- Operational choices for risk aggregation in insurance: PSDization and SCR sensitivity, IME Conference, Sydney (Australia), 07/2018;
- Lapse risk management in insurance, ANR LoLitA Conference, Paris (France), 01/2018;
- Microlevel-reserving with Machine Learning, a comparison, Colloquium AAI, Barcelona (Spain), 10/2017;
- Weighted decision trees applied to reserving in insurance, EAJ Conference, Lyon (France), 09/2016;
- Tree-based estimators for censored observations with actuarial applications, 12th ICOR, La Havana (Cuba), 03/2016;
- Stress tests for lapse risk: correlation and contagion among policyholders’ behaviours, CIRM Colloquium, Marseille, 02/2016;
- Mass lapse scenario in insurance, the use of a dynamic contagion process, L2 Seminar, 11/2015;
- Prediction of lifetimes by tree-based estimators, Longevity 11 Conference (Lyon), 09/2015;
- Rachats de contrats d’assurance et Solvency 2, Association Francaise de Gestion Actif-Passif, 03/2015;
- Risque de rachat en assurance, quelques approches, Chaire risques systémiques (ACPR), 01/2015;
- Surrenders: risk factors and modelling, Autorité du Controle Prudentiel et de Résolution (ACPR, french supervisor), 11/2014;
- Tree estimators in censored regression: application to reserving, EAJ Conference (Vienna, Austria), 09/2014.
- Selection of GLM mixtures with a clustering approach, MBC2 Workshop (Catania, Sicilia), 09/2014.
- Regression trees and duration models, Summer School of the Institute of Actuaries (Paris), 07/2014.
- Clustering with mixtures of GLM, 46th Journées de Statistique (Rennes, France), 06/2014.
- Whole life contract lifetime: prediction of lapses, IME Conference Copenhagen, Denmark, 07/2013.
- Surrenders in a competing risks framework, application with the [FG99] model, AFIR/ERM-PBSS-LIFE Colloquim, Lyon, France, 06/2013.
- Modelling the heterogeneity of surrender behaviours by using GLM mixtures, ASTIN-AFIR-IAALS Congress; Mexico city, Mexico, 10/2012.
- GLM mixture models to manage the complexity of surrender's behaviour modelling, 15th IME seminar held in Trieste (Italy), 06/2011.
- Classification et predictions of surrender risk, Journées Modélisation Aléatoire et Statistique (MAS) in Bordeaux (France), 09/2010.
- Surrender risk in life insurance, Summer school of the french institute of actuaries (Summer school) in Lyon (France), 07/2010.
- Surrender behaviours and copycat behaviours, SPAAF seminar, part of the ANR project AST&RISK in Lyon (France), 06/2010.
- Determining triggers of the surrender behaviours, Workshop ED SEG.
- Predicting surrender behaviours in saving business, SFdS (french association of statisticians) seminar held in Marseille (France), 05/2010.
- Using copulas in protection and health insurance, Sépia seminar (Paris, France), 03/2010.
I am member of the Editorial Board of Risks.
I reviewed a lot of papers in many journals in Statistics, Probability Theory and Actuarial Sciences. Here is a non-exhaustive list of these journals:
- Advances in Data Analysis and Classification,
- Electronic Journal of Statistics,
- Journal of Applied Probability (AP),
- Scandinavian Actuarial Journal (Scandinavian Actuarial Journal),
- Insurance: Mathematics and Economics (IME),
- ASTIN Bulletin (ASTIN),
- Journal of Statistical Software (JSS),
- Risks (Risks),
- European Actuarial Journal (EAJ),
- European Journal of Operational Research (EJOR).
I am currently supervising the PhD thesis of three students:
- Mathias Valla, jointly with Katrien Antonio (Professor at KU Leuven, Belgium). Mathias is working on adaptations of Machine Learning algorithms to insurance data (extremes, censoring, truncation, missing values);
- Pierre Chatelain, jointly with Stephane Loisel (Professor at ISFA, University of Lyon). Pierre is working on pricing in actuarial science taking into account data quality in pricing methods;
- Jean Brunet, jointly with Frederic Planchet (Professor at ISFA, University of Lyon). Jean is working on fully integrated reserving process, from data collection to risk management.
It is with great honnor that I received the following distinctions:
- SCOR 2013 Award (best PhD in Actuarial Science);
- best paper award (IAALS section) of the ASTIN-AFIR-IAALS congress (Mexico, 2012);
- 2011 Lloyd's Science of Risk Prize 2011: runner-up prize (insurance operations and markets) (with Stéphane Loisel).
Ph.D. thesis in Applied Mathematics
Title: GLM mixtures and selection of the number of components: application to surrender risk in life insurance. Defended on 07/06/2012, jury: H. Albrecher (president), B. Garel and D. Pommeret (referees), V. Maume-Deschamps and S. Loisel (supervisors), and V. Lepez (examinator).
Slides (defense): here.
Actuarial thesis at AXA Global Life (AGL, AXA Insurance Company):
Segmentation and modelling of surrender behaviours in life insurance. File here.