Stéphane Loisel

Claude Bernard University Lyon 1 | UCBL · Institut de science financière et d'assurances

This study addresses a research gap in quantitative modeling framework and scenario analysis for the risk management of stable value fund wraps, a crucial segment of the U.S. financial market with over USD $400 billion in assets. In this paper, we present an asset–liability model that encompasses an innovative approach to modeling the assets of fix...

In this paper, we investigate the behavioral and statistical characteristics of cash flows for stable value funds provided by numerous U.S. employee benefit plans. We analyze participant-initiated aggregated cash flow data, representing approximately 80% of the market for large employer plans with stand-alone stable value wraps within a 401(k) offe...

The major economic and health consequences of COVID-19 called for various protective measures and mass vaccination campaigns. A previsional model was used to predict the future impacts of various measure combinations on COVID-19 mortality over a 400-day period in France. Calibrated on previous national hospitalization and mortality data, an agent-b...

We study the problem of approximating the copula and copula density function from a sequence of transformed moments. In particular, when frequency moments of an underlying bivariate distribution are available, the uniform convergence of the reconstructed copula and the rate of approximation of the copula density function are obtained. Finally, the...

This paper proposes a method for quantifying the basis risk present in index-based insurance. It applies when the inherent uncertainty is represented by a randomly scaled variable. This turns out to be a reasonable assumption in a number of practical situations. Several properties of such a variable are first briefly studied. Their order in the s-c...

In this paper, we extend the non-cooperative one-period game of Dutang et al. (2013) to model a non-life insurance market over several periods by considering the repeated (one-period) game. Using Markov chain methodology, we derive general properties of insurer portfolio sizes given a price vector. In the case of a regulated market (identical premi...

Predicting the evolution of mortality rates plays a central role for life insurance and pension funds. Various stochastic frameworks have been developed to model mortality patterns by taking into account the main stylized facts driving these patterns. However, relying on the prediction of one specific model can be too restrictive and can lead to so...

The outbreak of the SARS-CoV-2 virus, enhanced by rapid spreads of variants, has caused a major international health crisis, with serious public health and economic consequences. An agent-based model was designed to simulate the evolution of the epidemic in France over 2021 and the first six months of 2022. The study compares the efficiencies of fo...

Modeling policyholders’ lapse behaviors is important to a life insurer, since lapses affect pricing, reserving, profitability, liquidity, risk management, and the solvency of the insurer. In this paper, we apply two machine learning methods to lapse modeling. Then, we evaluate the performance of these two methods along with two popular statistical...

Background The outbreak of SARS-CoV-2 virus has caused a major international health crisis with serious consequences in terms of public health and economy. In France, two lockdown periods were decided in 2020 to avoid the saturation of intensive care units (ICU) and an increase in mortality. The rapid dissemination of variant SARS-CoV-2 VOC 202012/...

Predicting the evolution of mortality rates plays a central role for life insurance and pension funds. Various stochastic frameworks have been developed to model mortality patterns taking into account the main stylized facts driving these patterns. However, relying on the prediction of one specific model can be too restrictive and lead to some well...

The estimation of R0 , the so-called "basic reproductive ratio", of the COVID-19 pandemic is of particular importance to help decision-makers take the necessary safeguard measures to protect the population. In this work, we examine a method based on the successive estimation of R0 over 3 non-overlapping periods (beginning of lockdown, during lockdo...

Background Compartmental models help making public health decisions. They were used during the COVID-19 outbreak to estimate the reproduction numbers and predict the number of hospital beds required. This study examined the ability of closely related compartmental models to reflect equivalent epidemic dynamics. Methods The study considered three i...

Predicting the evolution of mortality rates plays a central role for life insurance and pension funds. Standard single population models typically suffer from two major drawbacks: on the one hand, they use a large number of parameters compared to the sample size and, on the other hand, model choice is still often based on in-sample criterion, such...

This paper is concerned with properties of Beta-unimodal distributions and their use to assess the basis risk inherent to index-based insurance or reinsurance contracts. To this extent, we first characterize s-convex stochastic orders for Beta-unimodal distributions in terms of the Weyl fractional integral. We then determine s-convex extrema for su...

In this paper, we propose and study a risk model with two types of claims in which the insurer may invest into a prevention plan which decreases the intensity of large claims without impacting the small claims. We identify a necessary and sufficient condition for insurers to use prevention if there is no surplus. If, in addition, the severity of la...

In this chapter, we explain how quickest detection algorithms can be useful for risk management in presence of seasonality. We investigate the problem of detecting fast enough cases when a call center will need extra staff in a near future with a high probability. We illustrate our findings on real data provided by a French insurer. We also discuss...

In this paper, we introduce a new multivariate dependence model that generalizes the standard Schur-constant model. The difference is that the random vector considered is partially exchangeable, instead of exchangeable, whence the term partially Schur-constant. Its advantage is to allow some heterogeneity of marginal distributions and a more flexib...

The Price of Longevity RiskThe Price of Longevity Risk In this article, we address the issue of the price of longevity risk. We begin by describing the risk of longevity and its components, distinguishing biometric, financial and regulatory aspects. We then explain the different valuation frameworks (actuarial, financial and regulatory), their comm...

Modeling policyholders lapse behaviors is important to a life insurer since lapses affect pricing, reserving, profitability, liquidity, risk management, as well as the solvency of the insurer. Lapse risk is indeed the most significant life underwriting risk according to European Insurance and Occupational Pensions Authority's Quantitative Impact St...

This article summarizes the main topics and findings from the Swiss Risk and Insurance Forum 2018. That event gathered experts from academia, insurance industry, regulatory bodies, and consulting companies to discuss the challenges arising from the impact of data science and, more generally, of digitalization to the insurance sector.

This article summarizes the main topics and findings from the Swiss Risk and Insurance Forum 2018. That event gathered experts from academia, insurance industry, regulatory bodies, and consulting companies to discuss the challenges arising from the impact of data science and, more generally, of digitalization to the insurance sector.

A quantum mechanics approach is proposed to model non-life insurance risks and to compute the future reserve amounts and the ruin probabilities. The claim data, historical or simulated, are treated as coming from quantum observables and analyzed with traditional machine learning tools. They can then be used to forecast the evolution of the reserves...

This paper is concerned with Schur-constant survival models for discrete random variables. Our main purpose is to prove that the associated partial sum process is a non-homogeneous Markov chain. This is shown in three different situations where the random variables considered take values in the sets 0, {0,1} or {0,…,m}, m ≥ 2. The property of Schur...

The current low interest rate environment and the coming into force of Solvency II raise questions about the stability of the life insurance industry in Europe and the sustainability of traditional insurance products. We use a data set built from French supervisory reports to investigate the drivers of the participation rates (equivalent to annual...

This is a summary of the main topics and findings from the Swiss Risk and Insurance Forum 2017. That event gathered experts from academia, insurance industry, regulatory bodies, and consulting companies to discuss past and current developments as well as future perspectives in dealing with asset-liability management for long-term insurance business...

This is a summary of the main topics and findings from the Swiss Risk and Insurance Forum 2017. That event gathered experts from academia, insurance industry, regulatory bodies, and consulting companies to discuss past and current developments as well as future perspectives in dealing with asset-liability management for long-term insurance business...

Is Longevity Risk Insurable? In this paper, we study the question of insurability of longevity risk thanks to an Enterprise Risk Management approach. We start by identifying the different components of longevity risk. Then, we present the different ways to model, measure and detection changes in this risk. Finally, we study the possible risk contro...

Models and forecasts of damage from wind storms are a major issue for insurance companies. In this article, we focus on the calculation sensitivity of return periods for extreme events. Numerous elements come into play, such as data quality (location of insured buildings, weather report homogeneity), missing updates (history of insurance portfolios...

This paper deals with finite sequences of exchangeable 0–1 random variables. Our main purpose is to exhibit the dependence structure between such indicators. Working with Kendall's representation by mixture, we prove that a convex order of higher degree on the mixing variable implies a supermodular order of same degree on the indicators, and conver...

We consider the minimax quickest detection problem of an unobservable time of change in the rate of an inhomogeneous Poisson process. We seek a stopping rule that minimizes the robust Lorden criterion, formulated in terms of the number of events until detection, both for the worst-case delay and the false alarm constraint. In the Wiener case, such...

A numerical method to compute multivariate probability distributions from their Laplace transform is presented. The method consists in an orthogonal projection of the probability density function with respect to a probability measure that belongs to Natural Exponential Family with Quadratic Variance Function (NEF-QVF). A particular link to Lancaste...

The Solvency II directive has introduced a specific so-called risk-neutral framework to valuate economic accounting quantities throughout European life insurance companies. The adaptation of this theoretical notion for regulatory purposes requires the addition of a specific criterion, namely market-consistency, in order to objectify the choice of t...

In this paper we propose a multivariate approach for forecasting pairwise mortality rates of related populations. The need for joint modeling of mortality rates is analyzed using a causality test. We show that for the datasets considered, the inclusion of national mortality information enhances predictions on its sub-populations. The investi- gated...

This is a summary of the main topics and findings from the Swiss Risk and Insurance Forum 2015. That event gathered experts from academia, insurance industry, regulatory bodies, and consulting companies to discuss the past and current developments and necessary next steps for dealing with old-age provision. Topics include the pension funding gap, d...

As the famous statistician George Box said, “All models are wrong, but some of them are useful”. The goal of the validation process is not to say whether a model is right or wrong. Besides, model elaboration and validation must be regarded as an ongoing process, whose goal is to continuously improve and update the model. In this chapter, we shall f...

Stakeholders’ behaviour has several impacts on model risk and model management. The asset side of the balance sheet may be impacted by feedback loops on financial markets. Customer behaviour is one of the top risks faced by a company. Consequently, it must be carefully addressed in the model. In addition to these behavioural risks that have to be t...

As more and more people believe that significant life extensions may come soon, should commonly used future mortality assumptions be considered prudent? We find here that commonly used actuarial tables for annuitants – as well as the Lee-Carter model – do not extrapolate life expectancy at the same rate for future years as for past years; instead t...

In this paper, our aim is to measure mortality rates which are specific to individual observable factors when these can change during life. The study is based on longitudinal data recording marital status and socio-professional features at census times, therefore the observation scheme is interval-censored since individual characteristics are only...

Motivated by seasonality and regime-switching features of some insurance claim counting processes, we study the statistical analysis of a Markov-modulated Poisson process featuring seasonality. We prove the strong consistency and the asymptotic normality of a maximum split-time likelihood estimator of the parameters of this model, and present an al...

In the present paper we develop recursive algorithms to evaluate the distribution of the net present value (abbreviated as “NPV”) of a health care contract. The duration of the program is a random variable representing the lifetime of an individual. We suggest a discrete time phase-type approach to model individual health care costs. In this approa...

For insurance companies, wind storms represent a main source of volatility, leading to potentially huge aggregated claim amounts. In this article, we compare different constructions of a storm index allowing us to assess the economic impact of storms on an insurance portfolio by exploiting information from historical wind speed data. Contrary to hi...

In risk management, the distribution of underlying random variables is not always entirely known. Sometimes, only the mean value and some shape information on the distribution (decreasingness, convexity . . .) are available. The present paper provides discrete convex extrema for several situations of this type. The starting point is the class of di...

In this paper, we obtain asymptotic ruin probabilities in two models where claim amounts become more and more adverse, because of phenomena such as climate change or some kind of sectorial inflation. The method we use also enables us to study a risk model in which claims have infinite mean. In such models, ruin probability can be controlled by a st...

A numerical method to approximate ruin probabilities is proposed within the frame of a compound Poisson ruin model. The defective density function associated to the ruin probability is projected in an orthogonal polynomial system. These polynomials are orthogonal with respect to a probability measure that belongs to Natural Exponential Family with...

Dans le secteur de l'assurance automobile, la décision de la Cour de Justice de l'Union européenne selon laquelle il n'est plus possible de pratiquer des tarifs selon le sexe de l'assuré, ainsi que la diffusion des dispositifs d'assurance aukilo etre, entraînent nécessairement une évolution de la gestion du risque. Dans cet article, on se base sur...

This paper introduces a class of Schur-constant survival models, of dimension n, for arithmetic non-negative random variables. Such a model is defined through a univariate survival function that is shown to be n-monotone. Two general representations are obtained, by conditioning on the sum of the n variables or through a doubly mixed multinomial di...

In this paper, we propose some characteristics of next-year impairments in a generic Black and Scholes framework, with one equity security, and under International Financial Reporting Standards (IFRS) rules. We derive expression for the probability of impairment event for an equity-security recognized in the available-for-sale category. Our decompo...

For insurance companies, wind storms represent a main source of volatility, leading to potentially huge aggregated claim amounts. In this article, we compare different constructions of a storm index allowing us to assess the economic impact of storms on an insurance portfolio by exploiting information from historical wind speed data. Contrary to hi...

This paper studies a new risk measure derived from the expected area in red introduced in Loisel (2005). Specifically, we derive various properties of a risk measure defined as the smallest initial capital needed to ensure that the expected time-integrated negative part of the risk process on a fixed time interval [0,T][0,T] (TT can be infinite) is...

The goal of this paper is to give recent results in risk theory presented at the Conference ”Journée MAS 2012” which took place in Clermont Ferrand. After a brief state of the art on ruin theory, we explore some particular aspects and recent results. One presents matrix exponential approximations of the ruin probability. Then we present asymptotics...

In a multi-dimensional risk model with dependent lines of business, we propose to allocate capital with respect to the minimization of some risk indicators. These indicators are sums of expected penal- ties due to the insolvency of a branch while the global reserve is either positive or negative. Explicit formulas in the case of two branches are ob...

In this paper we consider conditionally independent processes with respect to some dynamic factor. We study the mixing properties of such processes when conditioning is given with respect to unbounded memory of the factor. Our work is motivated by some real examples related to risk theory.

We formulate a noncooperative game to model competition for policyholders among non-life insurance companies, taking into account market premium, solvency level, market share and underwriting results. We study Nash equilibria and Stackelberg equilibria for the premium levels, and give numerical illustrations.

We study a new risk measure inspired from risk theory with a heat wave risk analysis motivation. We show that this risk measure and its sensitivities can be computed in practice for relevant temperature stochastic processes. This is in particular useful for measuring the potential impact of climate change on heat wave risk. Numerical illustrations...

The purpose of this paper is to point out that an asymptotic rule A + B/u for the ultimate ruin probability applies to a wide class of dependent risk processes, in continuous or discrete time. That dependence is incorporated through a mixing model in the individual claim amount distributions. Several special mixing distributions are examined in det...

We present a new model of loss processes in insurance. The process is a couple $(N, \, L)$ where $N$ is a univariate Markov-modulated Poisson process (MMPP) and $L$ is a multivariate loss process whose behaviour is driven by $N$. We prove the strong consistency of the maximum likelihood estimator of the parameters of this model, and present an EM a...

This paper is concerned with the class of distributions, continuous or discrete, whose shape is monotone of finite integer order t. A characterization is presented as a mixture of a minimum of t independent uniform distributions. Then, a comparison of t-monotone distributions is made using the s-convex stochastic orders. A link is also pointed out...

In a multi-dimensional risk model with dependent lines of business, we propose to allocate capital with respect to the minimization of some risk indicators. These indicators are sums of expected penal- ties due to the insolvency of a branch while the global reserve is either positive or negative. Explicit formulas in the case of two branches are ob...

In a multi-dimensional risk model with dependent lines of business, we propose to allocate capital with respect to the minimization of some risk indicators. These indicators are sums of expected penal-ties due to the insolvency of a branch while the global reserve is either positive or negative. Explicit formulas in the case of two branches are ob-...

In this paper, we introduce a new structured financial product: the so-called Life Nominal Chooser Swaption (LNCS). Thanks to such a contract, insurers could keep pure longevity risk and transfer a great part of interest rate risk underlying annuity portfolios to financial markets. Before the issuance of the contract, the insurer determines a confi...

This article investigates the latest developments in longevity-risk modelling, and explores the key risk management challenges for both the financial and insurance industries. The article discusses key definitions that are crucial for the enhancement of the way longevity risk is understood, providing a global view of the practical issues for longev...

In this talk, we describe several models with dependent risks and give some exact or asymptotic formulas for finite-time or infinite-time ruin probabilities. Considered models either feature correlation crises (which occur when risks that are independent in the classical regime suddenly become strongly correlated) or correlations obtained by mixtur...