The correlated chain-ladder method for reserving in case of correlated claims developments

2005 ◽  
Vol 27 (2) ◽  
pp. 315-322 ◽  
Author(s):  
Erhard Kremer
Keyword(s):  
Chain Ladder Method ◽  
Chain Ladder

A robust random coefficient regression representation of the chain-ladder method

2021 ◽  
pp. 1-32
Author(s):  
Ioannis Badounas ◽  
Apostolos Bozikas ◽  
Georgios Pitselis
Keyword(s):  
Linear Regression ◽  
Linear Regression Model ◽  
Random Coefficients ◽  
Regression Coefficients ◽  
Varying Coefficients ◽  
Statistical Procedures ◽  
Chain Ladder Method ◽  
Loss Reserving ◽  
Random Coefficient Regression ◽  
Chain Ladder

Abstract It is well known that the presence of outliers can mis-estimate (underestimate or overestimate) the overall reserve in the chain-ladder method, when we consider a linear regression model, based on the assumption that the coefficients are fixed and identical from one observation to another. By relaxing the usual regression assumptions and applying a regression with randomly varying coefficients, we have a similar phenomenon, i.e., mis-estimation of the overall reserves. The lack of robustness of loss reserving regression with random coefficients on incremental payment estimators leads to the development of this paper, aiming to apply robust statistical procedures to the loss reserving estimation when regression coefficients are random. Numerical results of the proposed method are illustrated and compared with the results that were obtained by linear regression with fixed coefficients.

scholarly journals Chain Ladder Method: Bayesian Bootstrap Versus Classical Bootstrap

2009 ◽  
Author(s):  
Gareth William Peters ◽  
Mario V. Wuthrich ◽  
Pavel V. Shevchenko
Keyword(s):  
Bayesian Bootstrap ◽  
Chain Ladder Method ◽  
Chain Ladder

scholarly journals The Mean Square Error of Prediction in the Chain Ladder Reserving Method (Mack and Murphy Revisited)

2006 ◽  
Vol 36 (02) ◽  
pp. 521-542 ◽  
Author(s):  
Markus Buchwalder ◽  
Hans Bühlmann ◽  
Michael Merz ◽  
Mario V. Wüthrich
Keyword(s):  
Time Series ◽  
Mean Square Error ◽  
Time Series Model ◽  
Mean Square ◽  
Chain Ladder Method ◽  
The Mean ◽  
Chain Ladder

We revisit the famous Mack formula [2], which gives an estimate for the mean square error of prediction MSEP of the chain ladder claims reserving method: We define a time series model for the chain ladder method. In this time series framework we give an approach for the estimation of the conditional MSEP. It turns out that our approach leads to results that differ from the Mack formula. But we also see that our derivation leads to the same formulas for the MSEP estimate as the ones given in Murphy [4]. We discuss the differences and similarities of these derivations.

scholarly journals Neural Networks for the Joint Development of Individual Payments and Claim Incurred

Risks ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 33
Author(s):  
Łukasz Delong ◽  
Mario V. Wüthrich
Keyword(s):  
Neural Networks ◽  
Regression Models ◽  
Development Process ◽  
Real Data ◽  
Data Set ◽  
Joint Development ◽  
Chain Ladder Method ◽  
History Of ◽  
Feature Information ◽  
Chain Ladder

The goal of this paper is to develop regression models and postulate distributions which can be used in practice to describe the joint development process of individual claim payments and claim incurred. We apply neural networks to estimate our regression models. As regressors we use the whole claim history of incremental payments and claim incurred, as well as any relevant feature information which is available to describe individual claims and their development characteristics. Our models are calibrated and tested on a real data set, and the results are benchmarked with the Chain-Ladder method. Our analysis focuses on the development of the so-called Reported But Not Settled (RBNS) claims. We show benefits of using deep neural network and the whole claim history in our prediction problem.

scholarly journals Robustifying the multivariate chain-ladder method: A comparison of two methods

2016 ◽  
Vol 5 (1) ◽  
pp. 70-77
Author(s):  
Martine Van Wouwe ◽  
Nattakorn Phewchean
Keyword(s):  
Life Insurance ◽  
Higher Dimensions ◽  
Data Sets ◽  
Multiple Constraints ◽  
Insurance Company ◽  
Life Insurance Company ◽  
Robust Solutions ◽  
Higher Dimensional ◽  
Chain Ladder Method ◽  
Chain Ladder

The expected result of a non-life insurance company is usually determined for its activity in different business lines as a whole. This implies that the claims reserving problem for a portfolio of several (perhaps correlated) subportfolios is to be solved. A popular technique for studying such a portfolio is the chain-ladder method. However, it is well known that the chain-ladder method is very sensitive to outlying data. For the bivariate situation, we have already developed robust solutions for the chain-ladder method by introducing two techniques for detecting and correcting outliers. In this article we focus on higher dimensions. Being subjected to multiple constraints (no graphical plots available), the goal of our research is to find solutions to detect and smooth the influence of outlying data on the outstanding claims reserve in higher dimensional data sets. The methodologies are illustrated and computed for real examples from the insurance practice.

scholarly journals Credibility for the Chain Ladder Reserving Method

2008 ◽  
Vol 38 (02) ◽  
pp. 565-600 ◽  
Author(s):  
Alois Gisler ◽  
Mario V. Wüthrich
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Specific Data ◽  
Conjugate Priors ◽  
Chain Ladder Method ◽  
The Mean ◽  
Chain Ladder ◽  
Set Up ◽  
Classical Chain ◽  
Development Triangle

We consider the chain ladder reserving method in a Bayesian set up, which allows for combining the information from a specific claims development triangle with the information from a collective. That is, for instance, to consider simultaneously own company specific data and industry-wide data to estimate the own company's claims reserves. We derive Bayesian estimators and credibility estimators within this Bayesian framework. We show that the credibility estimators are exact Bayesian in the case of the exponential dispersion family with its natural conjugate priors. Finally, we make the link to the classical chain ladder method and we show that using non-informative priors we arrive at the classical chain ladder forecasts. However, the estimates for the mean square error of prediction differ in our Bayesian set up from the ones found in the literature. Hence, the paper also throws a new light upon the estimator of the mean square error of prediction of the classical chain ladder forecasts and suggests a new estimator in the chain ladder method.

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