Ruin problem in a changing environment and application to the cost of climate change for an insurance company

In this paper we obtain asymptotics for ruin probability in a risk model where claim size distribution as well as claim frequency change over time. This is a way to take into account observed and/or projected changes, due to climate change, in some specific weather-related events like tropical storms for instance. Some examples will be presented in order to illustrate the theory and start a discussion on the possible cost of climate change for an insurance company who wants to remain financially solvent

Copulas checker-type approximations: application to quantiles estimation of aggregated variables

International audienceEstimating high level quantiles of aggregated variables (mainly sums or weighted sums) is crucial in risk management for many application fields such as finance, insurance, environment... This question has been widely treated but new efficient methods are always welcome; especially if they apply in (relatively) high dimension. We propose an estimation procedure based on the checkerboard copula. It allows to get good estimations from a (quite) small sample of the multivariate law and a full knowledge of the marginal laws. This situation is realistic for many applications. Estimations may be improved by including in the checkerboard copula some additional information (on the law of a sub-vector or on extreme probabilities). Our approach is illustrated by numerical examples

On semiparametric estimation of ruin probabilities in the classical risk model

International audienceThe ruin probability of an insurance company is a central topic in risk theory.We consider the classical Poisson risk model when the claim size distribution and the Poisson arrival rate are unknown. Given a sample of inter-arrival times and corresponding claims, we propose a semiparametric estimator of the ruin probability. We establish properties of strong consistency and asymptotic normality of the estimator and study bootstrap confidence bands. Further, we present a simulation example in order to investigate the finite sample properties of the proposed estimator

Nonparametric statistical analysis of an upper bound of the ruin probability under large claims

In this paper, the classical Poisson risk model is considered. The claims are supposed to be modeled by heavy-tailed distributions, so that the moment generating function does not exist. The attention is focused on the probability of ruin. We first provide a nonparametric estimator of an upper bound of the ruin probability by Willmot and Lin. Then, its asymptotic behavior is studied. Asymptotic confidence intervals are studied, as well as bootstrap confidence intervals. Results for possibly unstable models are also obtained

Skew Generalized Extreme Value Distribution: Probability Weighted Moments Estimation and Application to Block Maxima Procedure

International audienceFollowing the work of Azzalini ([2] and [3]) on the skew normal distribution, we propose an extension of the Generalized Extreme Value (GEV) distribution, the SGEV. This new distribution allows for a better t of maxima and can be interpreted as both the distribution of maxima when maxima are taken on dependent data and when maxima are taken over a random block size. We propose to estimate the parameters of the SGEV distribution via the Probability Weighted Moments method. A simulation study is presented to provide an application of the SGEV on block maxima procedure and return level estimation. The proposed method is also implemented on a real-life data

Value at Risk estimation of aggregated risks using marginal laws and some dependence information

International audienceEstimating high level quantiles of aggregated variables (mainly sums or weighted sums) is crucial in risk management for many application fields such as finance, insurance, environment. . . . This question has been widely treated but new efficient methods are always welcome; especially if they apply in relatively) high dimension. We propose an estimation procedure based on the checkerboard copula. It allows to get good estimations from a quite) small sample of the multivariate law and a full knowledge of the marginal laws. This situation is realistic for many applications, mainly in insurance. Moreover, we may also improve the estimations by including in the checkerboard copula some additional information (on the lawof a sub-vector or on extreme probabilities)

Copulas checker-type approximations: application to quantiles estimation of aggregated variables

International audienceEstimating high level quantiles of aggregated variables (mainly sums or weighted sums) is crucial in risk management for many application fields such as finance, insurance, environment... This question has been widely treated but new efficient methods are always welcome; especially if they apply in (relatively) high dimension. We propose an estimation procedure based on the checkerboard copula. It allows to get good estimations from a (quite) small sample of the multivariate law and a full knowledge of the marginal laws. This situation is realistic for many applications. Estimations may be improved by including in the checkerboard copula some additional information (on the law of a sub-vector or on extreme probabilities). Our approach is illustrated by numerical examples