Chairs Days: Insurance, Actuarial Science, Data and Models

Date: June, 11 & 12 2018
Location: FFA – 26, Boulevard Haussmann – 75009 Paris

The Chairs of Excellence and the Research Initiative ACTINFO, ACTUARIAT DURABLE, DAMI and PREVENT’HORIZON with the FONDATION DU RISQUE
propose, for the first time, a two-day conference at the crossroads of themes that bring them together: Data Science and applications to insurance and finance (incomplete data, pricing, loss reserving, …), and Prevention and risks (risk perception, risk coverage and reduction, self-insurance, self-protection and insurance; public health and prevention, …).

Scientific Coordination:

Frédéric PLANCHET & Christian ROBERT  – DAMI Chair
Arthur CHARPENTIER & Romuald ELIE – ACTINFO Chair
Jean-Louis RULLIERE & Anne-Marie SCHOTT – PREVENT’HORIZON Chair
Stéphane LOISEL – IDR ACTUARIAT DURABLE

PROGRAMM

LINK TO THE SLIDES AND POSTERS

INVITED SPEAKERS

Katrien ANTONIO
Professor in Actuarial Science and insurance analytics at KU Leuven

Alexandre BOUMEZOUED
Head of R&D Milliman

Alfred GALICHON
Professor of Economics and of Mathematics at New-York University

Pierre-Yves GEOFFARD
Economist, Professor at Paris School of Economics

Meglena JELEVA
Professor of Economics at the University of Paris Nanterre

Julie JOSSE
Professor of Statistics at Ecole Polytechnique

Dylan POSSAMAI
Assistant Professor at Columbia University

Julien TRUFIN
Professor in Actuarial Science at ULB

Florian PELGRIN
Professor at Edhec Business School

TITLES AND ABSTRACTS

Data driven strategies for the construction of insurance tariff classes
Katrien ANTONIO, professor of Actuarial Science and Insurance Analytics at KU Leuven

Abstract: Insurance companies use predictive models for a variety of analytic tasks, including pricing, marketing campaigns, claims handling, fraud detection and reserving. Typically, these predictive models use a selection of continuous, ordinal, nominal and spatial risk factors to differentiate risks. Such models should not only be competitive, but also interpretable by stakeholders (including the policyholder and the regulator) and easy to implement and maintain in a production environment. That is why current actuarial literature puts focus on generalized linear models where risk cells are constructed by binning risk factors up front, using ad hoc techniques or professional expertise. In statistical literature penalized regression is often used to encourage the selection and fusion of predictors in predictive modeling. Most penalization strategies work for data where predictors are of the same type, such as LASSO for continuous variables and Fused LASSO for ordered variables. We design an estimation strategy for generalized linear models which includes variable selection and the binning of risk factors through L1-type penalties. We consider the joint presence of different types of covariates and a specific penalty for each type of predictor. Using the theory of proximal operators, our estimation procedure is computationally efficient since it splits the overall optimization problem into easier to solve sub-problems per predictor and its associated penalty. As such, we are able to simultaneously select, estimate and group, in a statistically sound way, any combination of continuous, ordinal, nominal and spatial risk factors. We illustrate the approach with simulation studies, and a case-study on motor insurance pricing.
This presentation will cover ongoing work by Katrien Antonio, Sander Devriendt, Edward (Jed) Frees, Roel Henckaerts, Tom Reynkens and Roel Verbelen.

Individual claims reserving: what’s new, what’s not?
Alexandre BOUMEZOUED, Head of R&D, Milliman

Abstract: The current reserving practice consists in most cases in using methods based on claims development triangles. However, several potential limits of aggregate methods based on triangles have already been highlighted both from a practical and a theoretical point of view. In the context of an increasing need of the market for more accurate reserving prediction and risk assessment, a proper use of the information embedded in individual claims data combined with appropriate individual claims development models represent a promising alternative. This session will review individual claims reserving models from their mathematical foundations to their practical use. Particular focus will be dedicated to the innovation opportunity raised by these alternative methods, and the tackling of the main challenges coming with their implementation.

Optimal transport tools for economics, finance and data science
Alfred GALICHON, Professor of Economics and of Mathematics at New-York University

Abstract: This talk, based on my recent book Optimal Transport Methods in Economics (Princeton, 2016), will provide an introduction to the theory of optimal transport, with a focus on applications to statistics and finance. The basic results in Optimal Transportation will be covered, and various applications to economics (labor markets), statistics (quantile methods and risk measures) and finance (martingale optimal transport) will be sketched.

Intertemporal moral hazard in car insurance
Pierre-Yves GEOFFARD, Economist, Professor at Paris School of Economics

Abstract: Standard moral hazard theory predicts that a better coverage against risks may induce less efforts to reduce these risks. However, when the characteristics of coverage depends on past accidents, such as in experience rating, the perspective of a better coverage or a lower premium in the future may induce more current efforts in risk reduction. We exploit a specific add-on feature of experience rating systems: the lifetime protection. When granted, under very restrictive conditions on past claims and seniority, the no claim discount of an insuree stays at its maximum level, no matter how many claims he may report. A contract with this feature hence offers a better dynamic cover against the risk of loss of no claim discount than a similar contract without it. We develop a dynamic moral hazard model to study the incentive changes between the two contracts. The contract with the better dynamic cover induces a lower or a higher effort depending on whether the insuree is granted with the lifetime protection. Protected insurees should report more claims, while unprotected ones should report less claims to increase their probability to be rewarded with the protection.
We exploit a very large data set on claims reported to a major insurance company in Ireland, which covers 132000 insurees, and contains 5.8 millions of observations on reported claims, from 2002 to 2007. We find evidence of moral hazard: protected insurees report 60\% more claims while unprotected ones report 10\% less. Anticipation occurs at least 6 months in advance. The effect on the protected ones is found for all type of at-fault claims, while the effect on the unprotected ones is found only for claims implying no third party. Women and insurees under 50 years are more reactive to incentives. This underlines the importance of taking into account dynamic effects of temporal changes in coverage.
Joint work with Alexandre Godzinski

Prevention and risk perception: theory and experiments
Meglena JELEVA, Professor of Economics at the University of Paris Nanterre

Abstract: Individual prevention decisions strongly depend on preferences and beliefs that can explain, at least partially, underinvestment in prevention activities. The rank dependant utility model, generalizing standard expected utility allows taking into account a broad range of risk perceptions and can be a relevant tool to better understand prevention decisions. In this presentation, we will first give some theoretical results about the impact of risk perceptions on primary and secondary individual prevention decisions. As an application of these results, we will analyze the trade-off between primary prevention and savings when individuals face a health (long-term care) risk and propose a public policy combining subsidies for prevention with a social insurance co-payment for long-term care expenditures. Our presentation will end with an experiment on the impact of risk communication on primary prevention against health risks resulting from air pollution.

Imputation of mixed data with multilevel singular value decomposition
Julie JOSSE, Professor of Statistics at Ecole Polytechnique

Abstract: Statistical analysis of large data sets o ers new opportunities to better understand many processes. Yet, data accumulation often implies relaxing acquisition procedures or compounding diverse sources. As a consequence, such data sets often contain mixed data, i.e. both quantitative and qualitative and many missing values. Furthermore, aggregated data present a natural multilevel structure, where individuals or samples are nested within di erent sites, such as countries or hospitals. Imputation of multilevel data has therefore drawn some attention recently, but current solutions are not designed to handle mixed data, and su er from important drawbacks such as their computational cost. In this work, we propose a single imputation method for multilevel data, which can be used to complete either quantitative, categorical or mixed data. The method is based on multilevel singular value decomposition (SVD), which consists in decomposing the variability of the data into two components, the between and within groups variability, and performing SVD on both parts. We show on a simulation study that
in comparison to competitors, the method has the great advantages of handling data sets of various size, and being computationally faster. Furthermore, it is the first so far to handle mixed data. We apply the method to impute a medical data set resulting from the aggregation of several data sets coming from di fferent hospitals.
This application falls in the framework of a larger project on Trauma patients. To overcome obstacles associated to the aggregation of medical data, we turn to distributed computation.

Employer-mandated complementary health insurance in France: the likely effect on social welfare
Florence JUSOT, Professor of Economics at University Paris dauphine

Abstract: In France, the Ani reform mandates all private sector employers to offer sponsored Complementary Health Insurance (CHI) to all of their employees beginning on January 1st, 2016. If this mandate may reduce the cost of CHI coverage for employees, it may also prevent them choosing their optimal level of coverage given their health care needs, their income and their risk preferences. Furthermore, as employees are on average in good health status, the mandate is going to deteriorate the health risk of the pool of insured covered by individual policies, which may increase premiums. Welfare of individuals not affected by the reform (as retired and long term unemployed) may thus decrease. Wages may also potentially decrease by the employer subsidy amount.
This research simulates the likely effects of this employer CHI mandate on the social welfare of the population making the most likely scenarios on the increase in individual policies premiums and the decrease in wages. It is based on the 2012 Health, Health Care and Insurance survey linked to the administrative data of the National Health Fund, which provides information on socio-economic characteristics, CHI, health status, risk preferences and health care expenditures.
The first results using an utilitarian social welfare function and an expected utility theory framework show that, if wages do not decrease and if we consider the lowest increase in individual CHI premiums, the Ani reform may induce a very weak increase in social welfare. This positive effect of the reform is mainly driven by the employer subsidy rather by the reduction of financial risk exposure and exists despite the loss of welfare of those who previously chose to be uninsured. However, as soon as we assume a decrease in wages by the employer subsidy, the reform may greatly reduce social welfare. The loss of welfare that may suffer insured on the CHI individual market is therefore hardly offset by the gain in welfare that may benefit private sector employees, while the former are more often vulnerable. There may be a lot of losers while the part of winners is rather small. Those first results will be completed by an additional analysis using an Atkinson social welfare function in order to explore the consequences of various degrees of inequalities aversion in the evaluation of this reform.
Joint work with Aurélie PIERRE.

Gaussian Process Models for Mortality Rates and Improvement Factors
Michael LUDKOVSKI, Professor of Statistics and Applied Probability at University of California Santa Barbara

Abstract: I will describe a Gaussian process (GP) framework for modeling mortality rates and mortality improvement factors. GP regression is a nonparametric, data-driven approach for determining the spatial dependence in mortality rates and jointly smoothing raw rates across dimensions, such as calendar year and age. This offers a machine learning alternative to existing Lee-Carter-type models that first enforce a parametric structure in the mortality surface and then overlay it with a time-series model. In our approach, the graduation and projection of longevity are unified into a single prediction operation, quantifying uncertainty associated with smoothed historical experience or generating full stochastic trajectories for out-of-sample forecasts. Moreover, the GP framework offers a joint treatment of the mortality rates and mortality improvement. It is also well suited for updating projections when newly available data arrives, and for dealing with « edge » issues where credibility is lower. We illustrate results with a detailed analysis of US mortality experience based on the CDC dataset, as well as UK and Japan data from the HMD. This is joint work with Jimmy Risk and Howard Zail.

Insurance, Prevention and Risk Attitudes: Experimental Analyzes
François PANNEQUIN, CREST and ENS Paris-Saclay

Abstract: We report several laboratory experiments highlighting the critical role of risk attitudes – risk aversion vs. risk loving – for insurance and prevention decisions.
In our experimental study of the insurance demand, risk averters seem roughly consistent with theoretical predictions while risk-seeking subjects exhibit behavior consistent with gambling and opportunism rather than a lack of interest in insurance. Moreover, for both risk averters and risk lovers, our experimental data comply with an all-or-nothing insurance behavior.
When subjects, in addition to insurance contracting, have the opportunity to invest in a loss-reduction technology, they substitute this type of prevention for insurance as soon as insurance pricing is going high. However, and contrary to the theoretical predictions, subjects do not equalize the marginal returns of both risk-hedging activities.
When insurance is compulsory, risk averters adjust (by substituting) their prevention behavior to compensate for the level (too high or too low) of the mandatory insurance coverage. By contrast, even though they would refuse to invest in any voluntary risk-hedging scheme, risk lovers freely invest in loss-reduction to supplement compulsory partial insurance coverage. Both our modeling and our experimental data support this counterintuitive result: for risk lovers, mandatory insurance enhances loss-reduction effort.
Joint experimental works with Anne Corcos (CURAPP-ESS UMR 7319 and Université de Picardie) and Claude Montmarquette (CIRANO and Université de Montréal).

Valuing Life as an Asset, as a Statistic and at Gunpoint
Florian PELGRIN, Professor at Edhec BusinessSchool

The Human Capital (HK), and Statistical Life Values (VSL) differ sharply in their empirical pricing of a human life and lack a common theoretical background, to justify these differences. We first contribute to the theory, and measurement of life value by providing a unified framework to formally define, and relate the Hicksian willingness to pay (WTP) to avoid changes in death risks, the HK, and the VSL. Second, we use this setting to introduce a benchmark life value calculated at Gunpoint (GPV), i.e. the maximal WTP to avoid certain, instantaneous death. Third, we associate a flexible human capital model to the common framework to characterize the WTP and the three life valuations in closed-form. Fourth, our structural estimates of these solutions yield life values of 8.35 M$ (VSL), 421 K$ (HK) and 447 K$ (GPV). We confirm that the strong curvature of the WTP, rather than the collective vs individual WTP or disjoint frameworks, explains why the VSL is much higher than other values.

An introduction to moral hazard in continuous time and applications
Dylan POSSAMAI, Columbia University

Abstract: this talk will be an introduction to recent progresses in the treatment of continuous-time principal-agent problems with moral hazard, as well as potential applications in insurance and finance.

Multivariate modelling of household claim frequencies in motor third-party liability insurance
Julien TRUFIN, Professor in Actuarial Science at ULB

Abstract: Actuarial risk classification studies are typically confined to univariate, policy-based analyses: individual claim frequencies are modelled for a single product, without accounting for the interactions between the different coverages bought by members of the same household. Now that large amounts of data are available and that the customer’s value is at the heart of insurers’ strategies, it becomes essential to develop multivariate risk models combining all the products subscribed by members of the household in order to capture the correlation effects. This study aims to supplement the standard actuarial policy-based approach with a household-based approach. This makes the actuarial model more complex but also increases the volume of available information which eases and refines forecasting. Possible cross-selling opportunities can also be identified.