Regression credibility estimator with two-level common effects

2019 ◽  
pp. 1-22
Author(s):  
Qiang Zhang ◽  
Ping Chen
Keyword(s):  
Credibility Estimator

scholarly journals Robust Credibility

1993 ◽  
Vol 23 (1) ◽  
pp. 117-143 ◽  
Author(s):  
Alois Gisler ◽  
Peter Reinhard
Keyword(s):  
Influence Function ◽  
Robust Statistics ◽  
Main Idea ◽  
Special Problem ◽  
Robust Estimator ◽  
Credibility Estimator ◽  
The Individual ◽  
The Right

AbstractOutlier observations caused by big claims or by an event producing a series of claims are a special problem in ratemaking and in tariff calculation. The authors believe that combining credibility and robust statistics is the right answer to this problem. The main idea is to robustify the individual claims experience by using a robust estimator Ti instead of the individual mean and to look at the credibility estimator based on the robust statistics {Ti: i = 1, 2, …} . Choosing a particular influence function leads to datatrimming with an observation-dependent trimming point.

A credibility-based yield forecasting model for crop reinsurance pricing and weather risk management

2019 ◽  
Vol 79 (1) ◽  
pp. 2-26 ◽  
Author(s):  
Wenjun Zhu ◽  
Lysa Porth ◽  
Ken Seng Tan
Keyword(s):  
Risk Management ◽  
Closed Form ◽  
Crop Yield ◽  
Forecasting Model ◽  
Content Type ◽  
Credibility Estimator ◽  
Weather Risk ◽  
Yield Forecasting ◽  
Crop Yield Forecasting ◽  
Weather Risk Management

Purpose The purpose of this paper is to propose an improved reinsurance pricing framework, which includes a crop yield forecasting model that integrates weather variables and crop production information from different geographically correlated regions using a new credibility estimator, and closed form reinsurance pricing formulas. A yield restatement approach to account for changing crop mix through time is also demonstrated. Design/methodology/approach The new crop yield forecasting model is empirically analyzed based on detailed farm-level data from Manitoba, Canada, covering 216 crop varieties from 19,238 farms from 1996 to 2011. As well, corresponding weather data from 30 stations, including daily temperature and precipitation, are considered. Algorithms that combine screening regression, cross-validation and principal component analysis are evaluated for the purpose of achieving efficient dimension reduction and model selection. Findings The results show that the new yield forecasting model provides significant improvements over the classical regression model, both in terms of in-sample and out-of-sample forecasting abilities. Research limitations/implications The empirical analysis is limited to data from the province of Manitoba, Canada, and other regions may show different results. Practical implications This research is useful from a risk management perspective for insurers and reinsurers, and the framework may also be used to develop improved weather risk management strategies to help manage adverse weather events. Originality/value This is the first paper to integrate a credibility estimator for crop yield forecasting, and develop a closed form reinsurance pricing formula.

scholarly journals Robust Methods for Credibility

1992 ◽  
Vol 22 (1) ◽  
pp. 33-49 ◽  
Author(s):  
Hans R. Künsch
Keyword(s):  
Robust Methods ◽  
Truncation Point ◽  
Credibility Estimator ◽  
Standard Linear

AbstractExcess claims lead to an unsatisfactory behavior of standard linear credibility estimators. We suggest in this paper to use robust methods in order to obtain better estimators. Our first proposal is the linear credibility estimator with the claims replaced by a robust M-estimator of scale calculed from the claims. This corresponds to a truncation of the claims with a truncation point depending on the data and different for each contract. We discuss the properties of the robust M-estimator and present several examples. In order to improve the performance for a very small number of years, we propose a second estimator, which incorporates information from other claims into the M-estimator.

scholarly journals Credibility Weighted Hazard Estimation

2000 ◽  
Vol 30 (2) ◽  
pp. 405-417 ◽  
Author(s):  
Jens Perch Nielsen ◽  
Bjørn Lunding Sandqvist
Keyword(s):  
Hilbert Space ◽  
Kernel Method ◽  
Sparse Data ◽  
Hazard Curve ◽  
Credibility Estimator ◽  
Space Projection ◽  
Hazard Estimation ◽  
Available Information ◽  
Nonparametric Kernel ◽  
Nonparametric Kernel Method

AbstractCredibility weighting is helpful in many insurance applications where sparse data crave information from other sources of data. In this paper we aim at estimating a hazard curve using the nonparametric kernel method, where a credibility weighting principle is used locally, so that areas of sparse data for one subgroup can be alleviated by available information from other subgroups. The credibility estimator is found through a Hilbert space projection formulation of Buhlmann-Straub's credibility approach.

A credibility method for profitable cross-selling of insurance products

2011 ◽  
Vol 6 (1) ◽  
pp. 65-75 ◽  
Author(s):  
Fredrik Thuring
Keyword(s):  
A Priori ◽  
Real Data ◽  
Risk Profile ◽  
Insurance Company ◽  
Data Set ◽  
Credibility Estimator ◽  
Insurance Product ◽  
Additional Product

AbstractA method is presented for identifying an expected profitable set of customers, to offer them an additional insurance product, by estimating a customer specific latent risk profile, for the additional product, by using the customer specific available data for an existing insurance product of the specific customer. For the purpose, a multivariate credibility estimator is considered and we investigate the effect of assuming that one (of two) insurance products is inactive (without available claims information) when estimating the latent risk profile. Instead, available customer specific claims information from the active existing insurance product is used to estimate the risk profile and thereafter assess whether or not to include a specific customer in an expected profitable set of customers. The method is tested using a large real data set from a Danish insurance company and it is shown that sets of customers, with up to 36% less claims than a priori expected, are produced as a result of the method. It is therefore argued that the proposed method could be considered, by an insurance company, when cross-selling insurance products to existing customers.

BAYESIAN CHAIN LADDER MODELS

2014 ◽  
Vol 45 (1) ◽  
pp. 75-99 ◽  
Author(s):  
Greg Taylor
Keyword(s):  
Credibility Estimator ◽  
Implicit Equations ◽  
Special Cases ◽  
Recursive Formulas ◽  
Error Terms ◽  
Map Estimator ◽  
The Cross ◽  
Chain Ladder ◽  
Ladder Models ◽  
Linear Bayes

AbstractThe literature on Bayesian chain ladder models is surveyed. Both Mack and cross-classified forms of the chain ladder are considered. Both cases are examined in the context of error terms distributed according to a member of the exponential dispersion family. Tweedie and over-dispersed Poisson errors follow as special cases. Bayesian cross-classified chain ladder models may randomise row, column or diagonal parameters. Column and diagonal randomisation has been largely absent from the literature until recently. The present paper allows randomisation of row and column parameters. The Bayes estimator, the linear Bayes (credibility) estimator, and the MAP estimator are shown to be identical in the Mack case, and in the cross-classified case provided that the error terms are Tweedie distributed. In the Mack case the variance structure is generalised considerably from the existing literature. In the cross-classified case the model structure differs somewhat from the existing literature, and a comparison is made between the two. MAP estimators for the cross-classified case are often given by implicit equations that require numerical solution. Recursive formulas are given for these in the general case of error terms from the exponential dispersion family. The connection between the cross-classified case and Bornhuetter-Ferguson prediction is explored.

scholarly journals Imprecise credibility theory

2021 ◽  
pp. 1-15
Author(s):  
Liang Hong ◽  
Ryan Martin
Keyword(s):  
Real World ◽  
Prior Information ◽  
Model Specification ◽  
Credibility Theory ◽  
Experience Rating ◽  
Credibility Estimator ◽  
Real World Applications ◽  
Property And Casualty Insurance ◽  
Doubly Robust ◽  
Interval Estimator

Abstract The classical credibility theory is a cornerstone of experience rating, especially in the field of property and casualty insurance. An obstacle to putting the credibility theory into practice is the conversion of available prior information into a precise choice of crucial hyperparameters. In most real-world applications, the information necessary to justify a precise choice is lacking, so we propose an imprecise credibility estimator that honestly acknowledges the imprecision in the hyperparameter specification. This results in an interval estimator that is doubly robust in the sense that it retains the credibility estimator’s freedom from model specification and fast asymptotic concentration, while simultaneously being insensitive to prior hyperparameter specification.

scholarly journals A CREDIBILITY APPROACH FOR COMBINING LIKELIHOODS OF GENERALIZED LINEAR MODELS

2016 ◽  
Vol 46 (3) ◽  
pp. 531-569 ◽  
Author(s):  
Marcus C. Christiansen ◽  
Edo Schinzinger
Keyword(s):  
Generalized Linear Models ◽  
Empirical Bayes ◽  
Linear Models ◽  
Claims Data ◽  
Model Fitting ◽  
Bayes Estimation ◽  
Credibility Estimator ◽  
Borrowing Strength ◽  
Insurance Claims Data ◽  
Mortality Modelling

AbstractGeneralized linear models are a popular tool for the modelling of insurance claims data. Problems arise with the model fitting if little statistical information is available. In case that related statistics are available, statistical inference can be improved with the help of the borrowing-strength principle. We present a credibility approach that combines the maximum likelihood estimators of individual canonical generalized linear models in a meta-analytic way to an improved credibility estimator. We follow the concept of linear empirical Bayes estimation, which reduces the necessary parametric assumptions to a minimum. The concept is illustrated by a simulation study and an application example from mortality modelling.

scholarly journals The Linear Markov Property in Credibility Theory

1987 ◽  
Vol 17 (1) ◽  
pp. 71-84 ◽  
Author(s):  
Thomas Witting
Keyword(s):  
Sufficient Conditions ◽  
Markov Property ◽  
Recent Time ◽  
Necessary And Sufficient Conditions ◽  
Credibility Theory ◽  
Experience Rating ◽  
Credibility Estimator ◽  
Time Period ◽  
Loss Reserving ◽  
Necessary And Sufficient

AbstractWe study the linear Markov property, i.e. the possibility of basing the credibility estimator on data of the most recent time period without loss of accuracy. Necessary and sufficient conditions are derived generally. The meaning of the linear Markov property is also discussed in different experience rating and loss reserving models.

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