相关论文: Modelling extreme claims via composite models and …

In many random phenomena, such as life-testing experiments and environmental data (like rainfall data), there are often positive values and an excess of zeros, which create modeling challenges. In life testing, immediate failures result in…

We revisit multivariate extreme value theory modeling by emphasizing multivariate regular variations and the multivariate Breiman Lemma. This allows us to recover in a simple framework the most popular multivariate extreme value…

We study the optimal decisions and equilibria of agents who aim to minimize their risks by allocating their positions over extremely heavy-tailed (i.e., infinite-mean) and possibly dependent losses. The loss distributions of our focus are…

Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…

Classical peaks over threshold analysis is widely used for statistical modeling of sample extremes, and can be supplemented by a model for the sizes of clusters of exceedances. Under mild conditions a compound Poisson process model allows…

Mixed modeling of extreme values and random effects is relatively unexplored topic. Computational difficulties in using the maximum likelihood method for mixed models and the fact that maximum likelihood method uses available data and does…

We study a new estimator for the tail index of a distribution in the Frechet domain of attraction that arises naturally by computing subsample maxima. This estimator is equivalent to taking a U-statistic over a Hill estimator with two order…

Claim reserving primarily relies on macro-level models, with the Chain-Ladder method being the most widely adopted. These methods were heuristically developed without minimal statistical foundations, relying on oversimplified data…

Empirical likelihood is a well-known nonparametric method in statistics and has been widely applied in statistical inference. The method has been employed by Lu and Peng (2002) to constructing confidence intervals for the tail index of a…

Extreme quantile regression provides estimates of conditional quantiles outside the range of the data. Classical quantile regression performs poorly in such cases since data in the tail region are too scarce. Extreme value theory is used…

This brief paper summarize the chances offered by the Peak-Over-Threshold method, related with analysis of extremes. Identification of appropriate Value at Risk can be solved by fitting data with a Generalized Pareto Distribution. Also an…

We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…

In a wide variety of sequential decision making problems, it can be important to estimate the impact of rare events in order to minimize risk exposure. A popular risk measure is the conditional value-at-risk (CVaR), which is commonly…

This paper considers estimation and inference about tail features when the observations beyond some threshold are censored. We first show that ignoring such tail censoring could lead to substantial bias and size distortion, even if the…

Panel data arise in a wide range of application areas, and developing modelling methods for extreme values under such a setup is essential for reliable risk assessment and management. When choosing to model the marginal distributions of…

We establish sharp large deviation asymptotics for the maximum order statistic of independent and identically distributed heavy-tailed random variables, valid for all Borel subsets of the right tail. This result yields exact decay rates for…

The claim experience of the past is a very important information to calculate the fair price of an insurance contract. In a lot of European countries for instance the prices for motor car insurance depend on the number of claims the driver…

Traditionally, actuaries have used run-off triangles to estimate reserve ("macro" models, on agregated data). But it is possible to model payments related to individual claims. If those models provide similar estimations, we investigate…

Often, it is required to estimate the probability that a quantity such as toxicity level, plutonium, temperature, rainfall, damage, wind speed, wave size, earthquake magnitude, risk, etc., exceeds an unsafe high threshold. The probability…

A discrete version of the Gumbel (Type I) extreme value distribution has been derived by using the general approach of discretization of a continuous distribution. Important distributional and reliability properties have been explored. It…