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Current research topics
My research is currently focused on the following themes:
The 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 so as to improve robustness).
- Machine Learning algorithms and applications to insurance,
- Stochastic models in actuarial science,
- Segmentation and classification methods,
- Survival analysis,
- Generalized linear models,
- Finite mixture models and semi-Markovian processes (hidden Markov models),
- Self-excited processes (like 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 (see publications below).
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 this famous models to competing risks models, an adequate framework to study endpoints (contract lifetime) in life insurance. A natural extension, still under study, concerns how to deal with censored 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 because 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.
Main published papers and 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, 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 Français 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:
- O. Lopez, X. Milhaud, P. Therond, Tree-based stochastic reserving in insurance.
- O. Lopez, X. Milhaud, Model selection of GLM mixtures with a clustering perspective.
- D. Pommeret, X. Milhaud, Y. Salhi, P. VanderkerkhoveComparison of Mixture Components.
- O. Lopez, X. Milhaud, Combining CART with LASSO techniques for insurance purpose.
- C. Genest, X. Milhaud, Aggregating correlated loss triangles, a credibility approach.
- 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.
Ph.D. thesis in Applied Mathematics
Title of the thesis:
GLM mixtures and number of components: application to surrender risk modelling in life insurance (here).
Slides (defense): here.
Actuarial thesis at AXA Global Life (AGL, AXA Insurance Company):
Segmentation and modelling of surrender behaviours in life insurance. File here.
I reviewed some papers in the following journals:
- 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),
- Bulletin Francais d'Actuariat (BFA).
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).