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Current research topics
My research is currently focused on the following themes:
The Ph.D. 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), with a focus on Random Forests technique so as to improve its robustness.
- 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 also natural, 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 behaviours, and compared this method with other classification algorithms in a discriminant analysis perspective (see publications below).
Concerning survival analysis, the main matters in my applications were about censorship and regression modelling. 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. A current extension, still under study, concerns how to deal with censored data in nonparametric regression techniques such as regression trees.
Recently I had to deal with problems like overdispersion and heterogeneity. This made me investigate another framework: finite mixture models, and their natural extension known as regime switching models. The point was firstly to think about potential applications on insurance datasets, and then to develop new results in terms of model selection in this framework. My coming research works should focus on GLM Markov switching models, as well as self-excited processes because they allow us to integrate dynamic correlation between agents.
Main published papers and talks
I would like to thank again my co-authors for these works...
...and the following talks (non exhaustive list):
- Published papers:
- Milhaud X., Exogenous and endogenous risk factors management to predict surrender behaviours, ASTIN Bulletin, (Sept. 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. Old HAL version
- 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 Franšais d'Actuariat (BFA), (2011) n.22, pp.5-48. Old HAL version
- 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 (Old link here).
- Submitted, in revision process, or working papers:
- O. Lopez, X. Milhaud, P. Therond, Consistency of tree-based estimators in censored regression with applications in insurance.
- O. Lopez, X. Milhaud, Model selection of GLM mixtures with a clustering perspective.
- F. Barsotti, X. Milhaud, Y. Salhi, Impact of interest rate movements on policyholders' behaviour in life insurance: contagion effect and massive surrenders.
- C. Dutang, X. Milhaud, Predicting surrenders as a competing risk: the subdistribution approach.
- O. Lopez, X. Milhaud, Combining CART with LASSO techniques for insurance purpose.
- O. Lopez, X. Milhaud, P. Therond, Reserving and claims' predictions with censored CART techniques.
- Tree estimators in censored regression: application to reserving, EAJ Conference (Vienna, Austria), September 2014.
- Selection of GLM mixtures with a clustering approach, MBC2 Workshop (Catania, Sicilia), September 2014.
- Regression trees and duration models, Summer School of the Institute of Actuaries (Paris), July 2014.
- Clustering with mixtures of GLM, 46th Journées de Statistique (Rennes, France), June 2014.
- Whole life contract lifetime: prediction of lapses, IME Conference Copenhagen, Denmark, July 2013.
- Surrenders in a competing risks framework, application with the [FG99] model, AFIR/ERM-PBSS-LIFE Colloquim, Lyon, France, June 2013.
- Modelling the heterogeneity of surrender behaviours by using GLM mixtures, ASTIN-AFIR-IAALS Congress; Mexico city, Mexico, October 2012.
- GLM mixture models to manage the complexity of surrender's behaviour modelling, 15th IME seminar held in Trieste (Italy), June 2011.
- Classification et predictions of surrender risk, Journées Modélisation Aléatoire et Statistique (MAS) in Bordeaux (France), September 2010.
- Surrender risk in life insurance, Summer school of the french institute of actuaries (Summer school) in Lyon (France), July 2010.
- Surrender behaviours and copycat behaviours, SPAAF seminar, part of the ANR project AST&RISK in Lyon (France), June 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), May 2010.
- Using copulas in protection and health insurance, Sépia seminar (Paris, France), March 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 memoir at AXA Global Life (AGL):
Segmentation and modelling of surrender behaviours in life insurance. File here.
I reviewed some papers in the following journals:
- European Actuarial Journal (EUAJ),
- European Journal of Operational Research (EJOR).
- Bulletin Franšais 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).