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Claims reserving is one of the most important actuarial tasks in non-life insurance modeling. There are several popular methods to perform claims reserving such as the chain-ladder (CL), the Bornhuetter--Ferguson (BF) or the generalized…
The paper proposes an original methodology for constructing quantitative statistical models based on multidimensional distribution functions constructed on the basis of the insurance companies' data on inshurance policies (including…
Insurers are faced with the challenge of estimating the future reserves needed to handle historic and outstanding claims that are not fully settled. A well-known and widely used technique is the chain-ladder method, which is a deterministic…
Due to the presence of reporting and settlement delay, claim data sets collected by non-life insurance companies are typically incomplete, facing right censored claim count and claim severity observations. Current practice in non-life…
The chain-ladder (CL) method is the most widely used claims reserving technique in non-life insurance. This manuscript introduces a novel approach to computing the CL reserves based on a fundamental restructuring of the data utilization for…
The prediction of future insurance claims based on observed risk factors, or covariates, help the actuary set insurance premiums. Typically, actuaries use parametric regression models to predict claims based on the covariate information.…
The sensitivity of loss reserving techniques to outliers in the data or deviations from model assumptions is a well known challenge. It has been shown that the popular chain-ladder reserving approach is at significant risk to such aberrant…
We introduce a continuous-time framework for the prediction of outstanding liabilities, in which chain-ladder development factors arise as a histogram estimator of a cost-weighted hazard function running in reversed development time. We use…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
Traditional techniques for calculating outstanding claim liabilities such as the chain ladder are notoriously at risk of being distorted by outliers in past claims data. Unfortunately, the literature in robust methods of reserving is scant,…
The appropriate estimation of incurred but not reported (IBNR) reserves is traditionally one of the most important task of actuaries working in casualty and property insurance. As certain claims are reported many years after their…
We propose a novel Bayesian nonparametric classification model that combines a Gaussian process prior for the latent function with a Dirichlet process prior for the link function, extending the interpretative framework of de Finetti…
This paper proposes a flexible and analytically tractable class of frequency and severity models for predicting insurance claims. The proposed model is able to capture nonlinear relationships in explanatory variables by characterizing the…
An insurance company is required to prepare a certain amount of money, called reserve, as a mean to pay its policy holders claims in the future. There are several types of reserve, one of them is IBNR reserve, for which the payments are…
The Chain-Ladder (CL) method remains the dominant macro-level technique for claims reserving in non-life insurance, yet its classical formulation lacks a coherent probabilistic foundation. Existing stochastic extensions-including the Mack…
The mean residual life function is a key functional for a survival distribution. It has a practically useful interpretation as the expected remaining lifetime given survival up to a particular time point, and it also characterizes the…
In reinsurance, Poisson and Negative binomial distributions are employed for modeling frequency. However, the incomplete data regarding reported incurred claims above a priority level presents challenges in estimation. This paper focuses on…
Spike-and-slab and horseshoe regression are arguably the most popular Bayesian variable selection approaches for linear regression models. However, their performance can deteriorate if outliers and heteroskedasticity are present in the…
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…
We revisit the famous Mack's model which gives an estimate for the conditional mean squared error of prediction of the chain-ladder claims reserves. We introduce a stochastic differential equation driven by a Brownian motion to model the…