**2017**

**MODELS FOR INSURANCE**

Measures of risk and performance in the management of insurance organizations > LONGEVITY

**Conditions of interest of a longevity megafund for pension funds, Debonneuil E., Eyraud-Loisel A., Planchet F. [2017], Working Paper, ISFA. Lien vers l’article**

Abstract: Pension funds that handle retirement risk need to invest assets in a diversified manner and on long durations while managing interest rate and longevity risk s. In the recent years, a new class of investment called a longevity megafund was described, that invests in clinical trials for solutions against age -related diseases. Using simple models, we here study the financial interest for pension funds of investing in a longevity megafund

Measures of risk and performance in the management of insurance organizations > MULTIVARIATE DEPENDENCE MODELING

**A central limit theorem for functions of stationary max-stable random fields on Rd, E. Koch, C. Bombry, C. Y. Robert Lien vers l’article**

Abstract: Max-stable random fields are very appropriate for the statistical modelling of spatial extremes. Hence, integrals of functions of max-stable random fields over a given region can play a key role in the assessment of the risk of natural disasters, meaning that it is relevant to improve our understanding of their probabilistic behaviour. For this purpose, in this paper, we propose a general central limit theorem for functions of stationary max-stable random fields on Rd. Then, we show that appropriate functions of the Brown-Resnick random field with a power variogram and of the Smith random field satisfy the central limit theorem. Another strong motivation for our work lies in the fact that central limit theorems for random fields on Rd have been barely considered in the literature. As an application, we briefly show the usefulness of our results in a risk assessment context.

**Infill asymptotics for estimators of the integral of the extreme value index function of the Brown-Resnick process, C. Y. Robert**

Abstract: We consider a max-stable process with a positive extreme value index function and an associated spectral process that is assumed to be a continuous exponential martingale. Both processes are regularly sampled on [0; 1] at high frequency n, with n going to infinity. We provide an estimator of the integral of the extreme value index function over [0; t], 0 < t < 1, and study its infill asymptotics properties. In particular, we show that the estimator is consistent, but we obtain a biased central limit theorem without hope of suitable bias correction. We then consider m iid sample-continuous stochastic processes that belong to the domain of attraction of the max-stable process and assume that these processes are also regularly sampled at rate 1=n. We show that the average values of the previous estimator built over the highest paths of these random elements can lead to an inconsistent estimator of the integral of the extreme value index function.

**Composite estimation method for Hierarchical Archimedean Copulas defined with multivariate compound distributions, H. Cossette, S-P. Gadoury, E. Marceau, C. Y. Robert**

Abstract: In the present paper, we examine in details the estimation procedure for the family of hierarchical Archimedean copulas proposed in Cossette et al. [3]. The hierarchical Archimedean copula construction is based on multivariate compound distributions, with the advantage of having no nesting conditions. We propose a top down composite likelihood approach: the parameters of the Archimedean copulas of the mothers (or the daughters) are given by the parameter of the mother (or the daughter) herself and the parameters of her ascendents. We are able to show the asymptotic normality of the estimators when the family tree is known. We are able to estimate the family tree by using the Górecki et al.[7]’s approach and combining it with a bootstrap procedure to decide whether it is necessary to groupe the binary structures. We use a GOF test to decide whether our estimated copula is close to the true copula even if the the family tree is not the true one. In other to preserve a flexible and general approach throughout the paper, we also introduce a new notation to define the family of hierarchical Archimedean copulas proposed in Cossette et al. [3]. Numerical examples are provided to illustrate the different steps of the estimation procedure.

**On a construction of multivariate distributions given some multidimensional marginals, D. Rulliere and N. Kazi-Tani Lien vers l’article**

Abstract: In this paper, we investigate the link between the joint law of a d-dimensional random vector and the law of some of its multivariate marginals. We introduce and focus on a class of distributions, that we call projective, for which we give detailed properties. This allows us to obtain necessary conditions for a given construction to be projective. We illustrate our results on elliptical distributions on the first hand, and on a new class of distribution having given bivariate margins on the other hand.

Measures of risk and performance in the management of insurance organizations > FINANCIAL MODELS AND MARKET CONSISTENCY

**Economic Scenario Generator with Five Factors, F****. Cheng & F. Planchet**

In this paper, we implement the stochastic deflator with five economic and financial factors: interest rates, market prices of risk, stock prices, default intensities, and convenience yields. We examine the deflator with different financial assets, such as stocks, zero‐coupon bonds, options, and corporate coupon bonds. Our numerical results show the reliability of the deflator approach in pricing financial derivatives.

**The impact of illiquidity on life insurance company asset allocation and selling strategy, ****Cousin, Y. Jiao, C. Y. Robert and O. D. Zerbib**

Abstract: The strong liquidity of many institutional investors liabilities, due to the surrender option giving policyholders the possibility of terminating their contracts at an early stage, has increased the risk of occurrence of illiquidity mismatches. The latter option adds considerable uncertainty to the timing and the magnitude of the liabilities cash flows for the insurance companies. The latter risk adds to the liquidity risk of financial assets and creates conditions favouring the fast deterioration of the asset owners solvency. For several economic reasons (such as the occurrence of a sharp increase in low interest rates, or in the insurance companies default risk), the lapse rate during a given period may become so high that insurance companies may have to sell off their assets. The obligation for insurers to reimburse the surrender values by making funds available immediately makes insurers especially vulnerable to the effects of transaction illiquidity. The concomitant effects of withdrawals and liquidity stress therefore force investors to sell their assets at a discounted price. This paper investigates the impact of illiquidity on insurance companies asset allocation and selling strategies.

Modelling policyholder behavior

**Predicting surrenders as a competing risk: the subdistribution approach, C. Dutang, X. Milhaud**

Robust proxies for use in calculating sensitivity and constituting model points, etc. to rapidly obtain assessments with reasonable calculation times

**Risk aggregation, PSDisation and SCR sensitivity by genetic algorithms, X. Milhaud, C. Saillard, soumis**

Abstract: This paper answers crucial questions about the robustness of the PSDisation process for applications in insurance. Using genetic algorithms, PSDisation refers to the process that forces a matrix to become positive semi-definite. For companies using copulas to aggregate risks in their internal model, PSDisation occurs when working with correlation matrices to compute the Solvency Capital Requirement (SCR). We study how classical operational choices concerning the modelling of risk dependence impacts the SCR during PSDisation. These operations refer to per- mutation of risks (or business lines) in the correlation matrix, addition of a new risk, and introduction of potential confidence weights given to some correlation co- efficients. It is shown that theoretically neutral transformations of the correlation matrix can surprisingly lead to significant changes of the SCR (up to 6%). This highlights the need for a very strong internal control around the PSDisation step.

**Reevaluation of the capital charge in insurance after a large shock: empirical and theoretical views, F. Borel-Mathurin, S. Loisel, J. Segers, Working paper (2017). Lien vers l’article**

Abstract: Motivated by the recent introduction of regulatory stress tests in the Solvency II framework, we study the impact of the re-estimation of the tail risk and of loss absorbing capacities on post-stress solvency ratios. Our contribution is threefold. First, we build the first stylized model for re-estimated solvency ratio in insurance. Second, this leads us to solve a new theoretical problem in statistics: what is the asymptotic impact of a record on the re-estimation of tail quantiles and tail probabilities for classical extreme value estimators? Third, we quantify the impact of the re-estimation of tail quantiles and of loss absorbing capacities on real-world solvency ratios thanks to regulatory data from EIOPA. Our analysis sheds a first light on the role of the loss absorbing capacity and its paramount importance in the Solvency II capital charge computations. We conclude with a number of policy recommendations for insurance regulators.

**DATA ANALYTICS IN INSURANCE**

Modern analytics methodologies

**Self Organizing Map for non-life insurances, D. Hainaut**

This research article proposes a framework based on neural map to analyse the geography of risks of a non-life insurance portfolio. Several extensions are proposed. First, we introduce a new metric for analysing qualitative variables. Second, we propose a credibility approach for explaining the low frequency of claims. Third, we propose a regression algorithm. The method is tested on a database of motorcycle claims. This work is related to the theme “data analytics for insurance” of the DAMI chair.

**Non parametric individual claims reserving in insurance, M. Baudry and C. Y. Robert Lien vers l’article**

Abstract: Accurate loss reserves are an important item in the financial statement of an insurance company and are mostly evaluated by macro-level models with aggregate data in run-o¤ triangles. In recent years, a new set of literature has considered individual claims data and proposed parametric reserving models based on claim history profiles. In this paper, we present a non parametric and flexible approach to estimate outstanding liabilities using all the covariables associated to the policy, its policyholder as well as all the informations received by the insurance company on the individual claim since its reporting date. The choice for a non parametric model leads to new issues since the target variables (claim occurrence and claim severity) are right-censored most of the time. The performance of our approach is evaluated by comparing the predictive values of the reserve estimates with their true values on simulated data. We also compare our individual approach with the most used aggregate data method, Chain Ladder, with respect to the bias and the variance of the estimates.

**Multiple time series forecasting using quasi-randomized functional link neural networks, Cousin A., Moudiki T., Planchet F. [2018] Working Paper, ISFA. Lien vers l’article**

Abstract: We are interested in obtaining forecasts for multiple time series, by taking into account the potential nonlinear relationships between their observations. For this purpose, we use a specific type of regression model on an augmented dataset of lagged time series. This model is inspired from dynamic regression models (Pankratz (2012)), with the response variable’s lags included as predictors. This type of regression model is known as Random Vector Functional Link (RVFL) neural networks, and has been successfully applied to solving regression and classification problems. The novelty of our approach is to apply the RVFL model to multivariate time series, under two separate regularization constraints on the regression parameters.

**Model selection of GLM mixtures with a clustering perspective, O. Lopez, X. Milhaud Lien vers l’article**

Model-based clustering from finite mixtures of generalized linear models (GLM) is a challenging issue which has undergone many recent developments. In practice model selection is often performed with AIC or BIC penalized criteria, although simulations show that they tend to overestimate the actual dimension of the model. As an alternative, we adapt another existing strategy to GLM mixtures: it consists in adding an entropic term to the log-likelihood in order to select the best mixture model, where \best” should be understood as the best trade-off between the fit to data and some clustering confidence. We derive key properties about the convergence of the associated M-estimator using concentration inequalities. The consistency of the corresponding selection criterion naturally follows under some classical requirements on the penalty. Finally, simulations enable to corroborate our theoretical results in the GLM mixtures framework and shows the effectiveness of the method.

**Reserving and claims’ predictions with censored CART techniques, O. Lopez, X. Milhaud, P. Therond **

Data management and interactions with predictive models and simulations

**Recent developments of artificial neural networks in actuarial sciences, D. Hainaut**

ISBA research report “Recent developments of artificial neural networks in actuarial sciences.” In this document of 120 pages, I explore the capacities of neural network for modelling actuarial claims processes. The document counts four chapters. The first one present the structure of neural networks. The second chapter explore MCMC calibration of neural net. The third one present an application to life insurance. The last chapter proposes a version of Kohonen’s map adapted for insurance. This work is related to the axis “data analytics for insurance” of the DAMI chair.

# 2016

**Cluster size distributions of extreme values for the Poisson-Voronoï tessellation, ****Chenavier, N. and Robert, C. (2016) **

Dans ce papier, nous décrivons la façon dont des évènements extrêmes se regroupent dans l’espace. Ce type de modèle trouve des applications dans la modélisation de la répartition des pertes financières dans l’espace consécutives à des catastrophes naturelles.

**Rare event simulation with heavy tails and Archimedean copulas. Cossette, H., Marceau, E, Nguyen, H.Q. and Robert, C. (2016). **

Dans ce papier, nous proposons des méthodes efficaces de simulations d’évènements rares du type « perte agrégée dépasse un certain niveau » lorsque les pertes individuelles ont des distributions à queue épaisse et leur dépendance est modélisée par une copule archimédienne.

**Lapse tables for lapse risk management, a competing risks approach. C. Dutang, X. Milhaud**

Nous traitons de la question des comportements de rachat avec une vision nouvelle en assurance vie sur ce risque: la considération de risques compétitifs avec une approche sous-distribution. L’idée est d’isoler ce risque parmi les autres risques concurrents (décès, changement de prime, maturité du contrat, …) afin d’en avoir une meilleure évaluation statistique. Au final, la modélisation permet de créer des tables d’expérience de rachat directement utilisable par une compagnie d’assurance.

**Robust evaluation of SCR for participating life insurances under solvency II, D.Hainaut, P. Devolder 2017. Working paper, not submitted yet.**

This article proposes a robust framework to evaluate the solvency capital requirements (SCR) of a participating life insurance with death benefits. The preference for robustness arises from the ambiguity caused by model shortcomings and parameters misspecifications. To incorporate the uncertainty in the procedure of evaluation, we consider a set of potential equivalent pricing measures in the neighborhood of the real one.

**Internal Model in Life insurance: Application of Least Square Monte-Carlo in Risk Assessment, ****Nteukam T. O., Planchet F., Ren J. [2016], Les cahiers de recherche de l’ISFA, n°2014.12.**

**Individual reserving by CART techniques, O. Lopez, X. Milhaud, P. Therond**

Ce papier compare les approches standards de provisionnement (agrégée type Chain Ladder, Mack, … comme individuelle) avec une modélisation par arbre CART. Nous montrons par l’analyse des boni-mali, ainsi que par l’estimation même des provisions, une précision supérieure de notre algorithme d’apprentissage par rapport à ces méthodes standards. De plus, notre technique permet de segmenter nos sinistres en fonction d’informations endogènes et exogènes venant impacter les provisions des assureurs.

**Obfuscation and Trust: Experimental evidence on Insurance Demand with Multiple Distribution Channels, Claire MOUMINOUX, Jean-Louis RULLIERE, Stéphane LOISEL**

This paper aims at shedding light on an insurance consumer dilemma: being self-confident facing an large set of insurance policies or rather trusting into an intermediary who assists her decision making, according to different distribution channels with different information frames. The results show that trust level is the main determinant of distribution channel choices while information obfuscation is the first inefficiency source of the decision making.

**Working papers – Période 2015-2020**

**Working papers – ****Période 2010-2015**

**Nouveaux développements de la théorie du risque :**

Bienvenüe, A. & Robert C. (2014). “Likelihood based inference for high-dimensional extreme value distributions*”*.

Robert C. (2014). “Rare-event asymptotics for the number of exceedances of multiplicative factor models*”*.

Guillou, A., Loisel, S. & Stupfler, G. (2014) “Estimating the parameters of a seasonal Markov-modulated Poisson process*”*, Working paper. Preprint sur Hal.

Goffard, P.-O., Loisel, S. & Pommeret, D. (2013) “A polynomial expansion to approximate the ultimate ruin probability in the compound Poisson ruin model*”*, Working paper. Preprint sur Hal.

Denuit, M. & Rey-Fournier, B. “Uni- and multi-dimensional risk attitudes: a unifying approach”, submitted for publication.

Cousin, A. & Di Bernardino, E. “On multivariate extensions of conditional-tail-expectation”, submitted for publication.

Nguyen, Q.H. & Robert, C. “Series expansions for sums of independent Pareto random variables”, submitted for publication.

**Management du capital économique des compagnies d’assurances : **

Laïdi Y., & Planchet F. (2014) “Calibrating LMN Model to Compute Best

Estimates in Life Insurance”, *Les cahiers de recherche de l’ISFA*, n°2014.13.

Nteukam T. O., Planchet F., & Ren J. (2014) “Internal Model in Life insurance:

Application of Least Square Monte-Carlo in Risk Assessment”, *Les cahiers de recherche de l’ISFA*, n°2014.12.

Salhi, Y. Thérond, P.-E. (2014) “Alarm System for Credit Losses Impairment”, working-paper ISFA n° 2014.2

Le maistre A., & Planchet F. (2013) “A proposal of interest rate dampener for Solvency II Framework introducing a three factors mean reversion model”, *Les cahiers de recherche de l’ISFA*, n°2013.2.

Cenac, P. Loisel, S. Maume-Deschamps, V. & Prieur, C. (2013) “Risk indicators with several lines of business: comparison, asymptotic behavior and applications to optimal reserve allocation”, submitted for publication.

Félix, J.P., Salhi, Y. & Therond, P. “Modeling French GAAP impairment losses for market consistent valuation purposes”

Bienvenüe, A., Loisel, S. & Therond, P. “An examination of equity securities impairment criteria on a multi-period basis”

Ingram, D., Clot, D., Loisel S. & Agba G. “Risk attitudes and attitudes w.r.t. models”, Travail en cours

Gfeller, A. & Norberg, R. “Dynamic sensitivity analysis I: a comparative stud”.

Norberg, R “Risk sharing in life insurance and pensions”.

Norberg, R “Paradigms in life insurance*”*. Chapter in edited volume Modelling in

life insurance – a management perspective to be submitted to Springer.

Bonnin, F. Juillard, M. & Planchet, F. (2012) “Best Estimate Calculations of Savings Contracts by Closed Formulas – Application to the ORSA”, submitted for publication.

**Risques de défaut, de liquidité, risques démographiques :**

El Karoui, N. Loisel, S. & Salhi, Y. (2015) “Optimality of the CUSUM Procedure for the Poisson Process*”*, working paper

Laurent, J. P. Sestier, M. & Thomas, S. (2015). “Trading book and credit risk: how fundamental is the Basel review ?*” *working paper.

Armakola, A. & Laurent, J-P. (2015), “CCP default fund exposures and clearing

membership*”*, working paper.

Barsotti, F. Salhi, Y. & Milhaud, X. (2015) “Mass Lapse Scenario in Insurance, an Alternative to Solvency II Stress Tests”, working paper

Guibert Q. & Planchet F. (2014) “Non-Parametric Inference of Transition Probabilities Based on Aalen-Johansen Integral Estimators for Semi-Competing Risks Data: Application to LTC Insurance”, *Les cahiers de recherche de l’ISFA*, n°2014.14.

Bonnin F., De Clermont-Tonnerre A., Planchet F., Sapone D. & Tammar M. (2014), “Valeur économique de dettes subordonnées pour des sociétés non-vie” *Les cahiers de
recherche de l’ISFA*, n° 2014.15.

Tomas, J. & Planchet, F. (2013) “Prospective Mortality Tables: Taking Heterogeneity

Into Account”, Les cahiers de recherche de l’ISFA, 2013.5

Tomas, J. & Planchet, F. (2013) “Constructing entity specific prospective mortality

table: adjustment to a reference”. Cahiers de Recherche de l’ISFA, 2013(13), 1-32, submitted for publication.

Laurent, J-P. Amzelek P. & Bonnaud, J. (2013) “An overview of the valuation of

collateralized derivatives contracts”, in revision Review of Derivatives Research.

Salhi, Y. Therond, P. & Tomas, J. “*Makeham-Law Adjustment with application to dynamic-hedging of biometric risks*”

Lopez, O. Milhaud, X. & Therond, P. “Consistency of tree-based estimators in censored

regression with applications in insurance”

Croix, J.C. Planchet, F. & Therond, P. “Mortality: a statistical approach to detect model

misspecification” [preprint]

El Karoui, N. Loisel, S. & Salhi, Y. “Détection de fin de validité d’hypothèses actuarielles”

Norberg, R, “Forward mortality rates revisited”.

Bensusan, H. El Karoui, N. Loisel, S. & Salhi, Y. (2012) “Partial splitting of longevity and financial risks: the Longevity Nominal Choosing Swaptions”, working paper.

Bonnaud, J. Carlier, L. Laurent, J.P. & Vila, J-L. (2012) « Sovereign Recovery Schemes:

Discounting and Risk Management Issues”, working paper.

Hainaut, D. Robert, C. (2012) “Credit risk valuation with rating transitions and partial

information”. submitted for publication.

Salhi, Y. & Loisel, S. (2012) “Basis risk modelling: a co-integration based approach”

(former title: Joint modeling of portfolio experienced and national mortality: A co-integration based approach), working paper.