MILHAUD Xavier

In this paper, we consider two-component mixture distributions having one known component. This type of model is of particular interest when a known random phenomenon is contaminated by an unknown random effect. We propose in this setup to compare the unknown random sources involved in two separate samples. For this purpose, we introduce the so-called IBM (Inversion-Best Matching) approach resulting in a relaxed semiparametric Cramér-von Mises type two-sample test requiring very minimal assumptions (shape constraint free) about the unknown distributions. The accomplishment of our work lies in the fact that we establish a functional central limit theorem on the proportion parameters along with the unknown cumulative distribution functions of the model when Patra and Sen [22] prove that the √ n-rate cannot be achieved on these quantities in the basic one-sample case. An intensive numerical study is carried out from a large range of simulation setups to illustrate the asymptotic properties of our test. Finally, our testing procedure is applied to a real-life application through pairwise post-covid mortality effect testing across a panel of European countries.

We consider in this paper two-component mixture distributions having one known component. This is the case when a gold standard reference component is well known, and when a population contains such a component plus another one with different features. When two populations are drawn from such models, we propose a penalized Chi-squared type testing procedure able to compare pairwise the unknown components, i.e. to test the equality of their residual features densities. An intensive numerical study is carried out from a large range of simulation setups to illustrate the asymptotic properties of our test. Moreover the testing procedure is applied on two real cases: i) mortality datasets, where results show that the test remains robust even in challenging situations where the unknown component only represents a small percentage of the global population, ii) galaxy velocities datasets, where stars luminosity mixed with the Milky Way are compared.

Thanks to nonparametric estimators coming from machine learning, microlevel reserving has become more and more popular for actuaries. Recent research focused on how to integrate the whole information one can have on claims to predict individual reserves, with varying success due to incomplete observations. Using the CART algorithm, we develop new results that allow us to deal with large reporting delays and partially observed explanatory variables. Statistically speaking, we extend CART to take into account truncation of the data, and introduce plug-in estimators. Our applications are based on real-life insurance portfolios embedding Income Protection and Third-Party Liability guarantees. The full knowledge of the claim lifetime is shown to be crucial to predict the individual reserves efficiently.

Thanks to nonparametric estimators coming from machine learning, microlevel claim reserving has become more and more popular in actuarial sciences. Recent research has focused on how to integrate the whole information one can have on claims to predict individual reserves, with varying success due to incomplete observations. In this paper, we introduce three extensions to comparable existing works: how to deal with censoring and truncation present in such type of data, how to cope with inflation when the inflation factor is unknown, and how to implement an adequate strategy leading to robust personalized reserve estimates. Using independent test sets, our results-on guarantees with typical long development times-indicate the importance of using the total claim development time to predict the reserves with acceptable accuracy. To remain close to reality, our applications are based on two open portfolios based on real-life datasets.

In non-life insurance, business sustainability requires accurate and robust predictions of reserves related to unpaid claims. To this aim, two different approaches have historically been developed: aggregated loss triangles and individual claim reserving. The former has reached operational great success in the past decades, whereas the use of the latter still remains limited. Through two illustrative examples and introducing an appropriate tree-based algorithm, we show that individual claim reserving can be really promising, especially in the context of long-term risks.

This paper answers crucial questions about the robustness of the PSDization process for applications in insurance. PSDization refers to the process that forces a matrix to become positive semi-definite. For companies using copulas to aggregate risks in their internal model, PSDization 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 PSDization. These operations refer to permutations of risks (or business lines) in the correlation matrix, addition of a new risk, and introduction of confidence weights given to the correlation coefficients. Using genetic algorithms, it is shown that theoretically neutral transformations of the correlation matrix can surprisingly lead to significant sensitivities of the SCR (up to 6%). This highlights the need for a very strong internal control around the PSDization step.

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eThis paper deals with the crucial problem of modeling policyholders' behaviours in life insurance. We focus here on the surrender behaviours and model the contract lifetime through the use of survival regression models. Standard models fail at giving acceptable forecasts for the timing of surrenders because of too much heterogeneity, whereas the competing risk framework provides interesting insights and more accurate predictions. Numerical results follow from using Fine & Gray model ([13]) on an insurance portfolio embedding Whole Life contracts. Through backtests, this framework reveals to be quite efficient and recovers the empirical lapse rate trajectory by aggregating individual predicted lifetimes. These results could be particularly useful to design future insurance product. Moreover, this setting allows to calibrate experimental lapse tables, simplifying the lapse risk management for operational teams.

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We propose a regression tree procedure to estimate the conditional distribution of a variable which is not directly observed due to censoring. The model that we consider is motivated by applications in insurance , including the analysis of guarantees that involve durations, and claim reserving. We derive consistency results for our procedure, and for the selection of an optimal subtree using a pruning strategy. These theoretical results are supported by a simulation study, and two applications involving insurance datasets. The first concerns income protection insurance, while the second deals with reserving in third-party liability insurance.

Implementation of regression tree and classification methods in the presence of right-censored data in the context of the provisioning of the risk of work stoppage by an insurer.

The present paper proposes a new methodology to model the lapse risk in life insurance by integrating the dynamic aspects of policyholders’ behaviors and the dependency of the lapse intensity on macroeconomic conditions. Our approach, suitable to stable economic regimes as well as stress scenarios, introduces a mathematical framework where the lapse intensity follows a dynamic contagion process, see [Dassios A. and Zhao H. (2011): A dynamic contagion process, Advances in Applied Probability, Vol. 43:3, p. 814–846]. This allows to capture both contagion and correlation potentially arising among insureds’ behaviors. In this framework, an external market driven jump component drives the lapse intensity process depending on the interest rate trajectory: when the spread between the market interest rates and the contractual crediting rate crosses a given threshold, the insurer is likely to experience more surrenders. A log-normal dynamic for the forward rates is introduced to build trajectories of an observable market variable and mimic the effect of a macroeconomic triggering event based on interest rates on the lapse in- tensity. Contrary to previous works, our shot-noise intensity is not constant and the resulting intensity process is not Markovian. Closed-form expressions and analytic sensitivities for the moments of the lapse intensity are provided, showing how lapses can be affected by massive copycat behaviors. Further analyses are then conducted to illustrate how the mean risk varies depending on the model’s parameters, while a simulation study compares our results with those obtained using standard practices. The numerical outputs highlight a potential misestimation of the expected number of lapses under extreme scenarios when using classical stress testing methodologies.

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These tools provide new methods to respond to the problems of insurers, particularly for the analysis of policyholder and prospect behavior. They allow the construction of risk classes.

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Model-based clustering from finite mixtures of generalized linear models is a challenging issue which has undergone many recent developments. In practice, the model selection step is usually performed by using AIC or BIC penalized criteria. Though, simulations show that they tend to overestimate the actual dimension of the model. These evidence led us to consider a new criterion close to ICL, firstly introduced in Baudry (2009). Its definition requires to introduce a contrast embedding an entropic term: using concentration inequalities, we derive key properties about the convergence of the associated M-estimator. The consistency of the corresponding classification criterion then follows depending on some classical requirements on the penalty term. Finally a simulation study enables to corroborate our theoretical results, and shows the effectiveness of the method in a clustering perspective.

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Insurers have been concerned about surrenders for a long time especially in Saving business, where huge sums are at stake. The emergence of the European directive Solvency II, which promotes the development of internal risk models (among which a complete unit is dedicated to surrender risk management), strengthens the necessity to deeply study and understand this risk. In this paper we investigate the topics of segmenting and modeling surrenders in order to better take into account the main risk factors impacting policyholders' decisions. We find that several complex aspects must be specifically dealt with to predict surrenders, in particular the heterogeneity of behaviour as well as the context faced by the insured. Combining them, we develop a new methodology that seems to provide good results on given business lines, and that moreover can be adapted for other products with little effort.

The issue of surrender has long been of concern to insurers, particularly in the context of life insurance savings contracts, for which colossal sums are at stake. The emergence of the European Solvency II directive, which recommends the development of internal models (of which an entire module is dedicated to the management of surrender behavior risks), reinforces the need to deepen our knowledge and understanding of this risk. It is in this context that we address in this thesis the issues of segmentation and modeling of surrenders, with the objective of better understanding and taking into account all the key factors that influence policyholders' decisions. The heterogeneity of behaviors and their correlation, as well as the environment to which policyholders are subjected, are as many difficulties to be treated in a specific way in order to make forecasts. We have developed a methodology that has produced very encouraging results and has the advantage of being replicable by adapting it to the specificities of different product lines. Through this modeling, model selection appears as a central point. We address it by establishing the strong convergence properties of a new estimator, as well as the consistency of a new selection criterion within the framework of mixtures of generalized linear models. Insurers have been concerned about surrenders for a long time especially in Saving business, where huge sums are at stake.

The issue of surrender has long been of concern to insurers, particularly in the context of life insurance savings contracts, for which colossal sums are at stake. The emergence of the European Solvency II directive, which recommends the development of internal models (of which an entire module is dedicated to the management of surrender behavior risks), reinforces the need to deepen our knowledge and understanding of this risk. It is in this context that we address in this thesis the issues of segmentation and modeling of surrenders, with the objective of better understanding and taking into account all the key factors that influence policyholders' decisions. The heterogeneity of behaviors and their correlation, as well as the environment to which policyholders are subjected, are as many difficulties to be treated in a specific way in order to make forecasts. We have developed a methodology that has produced very encouraging results and has the advantage of being replicable by adapting it to the specificities of different product lines. Through this modeling, model selection appears as a central point. We address it by establishing the strong convergence properties of a new estimator, as well as the consistency of a new selection criterion in the context of mixtures of generalized linear models.