scholarly journals The Measures of Accuracy of Claim Frequency Credibility Predictor

2021 ◽  
Vol 13 (21) ◽  
pp. 11959
Author(s):  
Alicja Wolny-Dominiak ◽  
Tomasz Żądło
Keyword(s):  
Life Insurance ◽  
Mixed Models ◽  
Linear Mixed Models ◽  
Parametric Bootstrap ◽  
Credibility Theory ◽  
Insurance Companies ◽  
Green Technologies ◽  
Claim Frequency ◽  
Bootstrap Algorithm ◽  
Insurance Data

Nowadays, the sustainability risks and opportunities start to affect strongly insurance companies in regard to the resulting additional variability of future values of variables taken into account in the decision processes. This is important especially in the era of sustainable non-life insurance promoting, among others, the use of ecological car engines or ecological systems of building heating. The fundamental issue in non-life insurance is to predict future claims (e.g., the aggregate value of claims or the number of claims for a single policy) in a heterogeneous portfolio of policies taking account of claim experience. For this purpose, the so-called credibility theory is used, which was initiated by the fundamental Bühlmann model modified to the Bühlmann–Straub model. Several modifications of the model have been proposed in the literature. One of them is the development of the relationship between the credibility models and statistical mixed models (e.g., linear mixed models) for longitudinal data. The article proposes the use of the parametric bootstrap algorithm to estimate measures of accuracy of the credibility predictor of the number of claims for a single policy taking into account new risk factors resulting from the emergence of green technologies on the considered market. The predictor is obtained for the model which belongs to the class of Generalised Linear Mixed Models (GLMMs) and which is a generalization of the Bülmann–Straub model. Additionally, the possibility of predicting the number of claims and the problem of the assessment of the prediction accuracy are presented based on a policy characterized by new green risk factor (hybrid motorcycle engine) not previously present in the portfolio. The paper presents the proposed methodology in a case study using real insurance data from the Polish market.

V The Verification of Technical Reserves in Non-Life Insurance

1971 ◽  
Vol 20 (01) ◽  
pp. 51-53
Author(s):  
C. M. Stewart
Keyword(s):  
Life Insurance ◽  
Risk Groups ◽  
Insurance Companies ◽  
Life Assurance ◽  
Careful Scrutiny ◽  
Sufficient Detail ◽  
Satisfactory Method ◽  
Claim Frequency ◽  
The Government ◽  
Do So

The reader of this note will know well the method used in the U.K. for the verification of technical reserves (i.e. the net liability) in life assurance. The net liability must be calculated by a qualified actuary and the methods and bases used must be described in sufficient detail in Schedule 4 of The Insurance Companies (Accounts and Forms) Regulations 1968 for their suitability to be apparent from a careful scrutiny of these and the other financial statistics submitted in accordance with the Regulations. As the data are made public, this scrutiny can be made not only by the Government Actuary in advising the supervisory authorities at the Department of Trade and Industry, but also by any other qualified actuary who cares to do so, which is an equally important discipline. Under this system, the maximum freedom can be allowed to the company and its actuary, but there has hitherto been no equally satisfactory method available for the objective scrutiny of non-life technical reserves. However, the new Claim Frequency Analyses and Claim Settlement Analyses prescribed in Parts II and III of Schedule 3 to the 1968 Regulations should go a long way towards remedying this deficiency. These analyses are to be supplied separately for each class of insurance in each of a company's main markets, and separately for such risk groups within each class as the company decides to be appropriate.

scholarly journals An Application of Credibility Theory to Solvency Margins: Some Comments on a Paper by G. W. De Wit and W. M. Kastelijn

1982 ◽  
Vol 13 (1) ◽  
pp. 37-46 ◽  
Author(s):  
Henrik Ramlau-Hansen
Keyword(s):  
Life Insurance ◽  
Alternative Methods ◽  
Credibility Theory ◽  
Insurance Companies ◽  
Numerical Example

AbstractSome comments are given on a recent paper by de Wit and Kastelijn (1980) and alternative methods for analysing loss ratios are proposed in connection with the determination of the necessary solvency margins of non-life insurance companies. The methods are illustrated by a numerical example.

Generalized linear mixed models for multi-reader multi-case studies of diagnostic tests

2015 ◽  
Vol 26 (3) ◽  
pp. 1373-1388 ◽  
Author(s):  
Wei Liu ◽  
Norberto Pantoja-Galicia ◽  
Bo Zhang ◽  
Richard M Kotz ◽  
Gene Pennello ◽  
...  
Keyword(s):  
Mixed Models ◽  
Diagnostic Tests ◽  
Fixed Effects ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Generalized Linear Mixed Models ◽  
Characteristic Curve ◽  
Linear Mixed Models ◽  
Parametric Bootstrap ◽  
Pseudo Likelihood

Diagnostic tests are often compared in multi-reader multi-case (MRMC) studies in which a number of cases (subjects with or without the disease in question) are examined by several readers using all tests to be compared. One of the commonly used methods for analyzing MRMC data is the Obuchowski–Rockette (OR) method, which assumes that the true area under the receiver operating characteristic curve (AUC) for each combination of reader and test follows a linear mixed model with fixed effects for test and random effects for reader and the reader–test interaction. This article proposes generalized linear mixed models which generalize the OR model by incorporating a range-appropriate link function that constrains the true AUCs to the unit interval. The proposed models can be estimated by maximizing a pseudo-likelihood based on the approximate normality of AUC estimates. A Monte Carlo expectation-maximization algorithm can be used to maximize the pseudo-likelihood, and a non-parametric bootstrap procedure can be used for inference. The proposed method is evaluated in a simulation study and applied to an MRMC study of breast cancer detection.

scholarly journals Extension and Application of Credibility Models in Predicting Claim Frequency

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Yuan-tao Xie ◽  
Zheng-xiao Li ◽  
Rahul A. Parsa
Keyword(s):  
Mixed Models ◽  
Negative Binomial ◽  
Generalized Linear Mixed Models ◽  
Linear Mixed Models ◽  
Actuarial Science ◽  
Underlying Assumption ◽  
Binomial Distributions ◽  
Numerical Studies ◽  
Proposed Model ◽  
Claim Frequency

In nonlife actuarial science, credibility models are one of the main methods of experience ratemaking. Bühlmann-Straub credibility model can be expressed as a special case of linear mixed models (LMMs) with the underlying assumption of normality. In this paper, we extend the assumption of Bühlmann-Straub model to include Poisson and negative binomial distributions as they are more appropriate for describing the distribution of a number of claims. By using the framework of generalized linear mixed models (GLMMs), we obtain the generalized credibility premiums that contain as particular cases another credibility premium in the literature. Compared to generalized linear mixed models, our extended credibility models also have an advantage in that the credibility factor falls into the range from 0 to 1. The performance of our models in comparison with an existing model in the literature is also evaluated through numerical studies, which shows that our approach produces premium estimates close to the optima. In addition, our proposed model can also be applied to the most commonly used ratemaking approach, namely, the net, the optimal Bonus-Malus system.

scholarly journals PERHITUNGAN PREMI ASURANSI JIWA MENGGUNAKAN GENERALIZED LINEAR MIXED MODELS

2019 ◽  
Vol 4 (2) ◽  
pp. 80
Author(s):  
Siti Alfiatur Rohmaniah ◽  
Novita Eka Chandra
Keyword(s):  
Life Insurance ◽  
Mixed Models ◽  
Generalized Linear Mixed Models ◽  
Linear Mixed Models ◽  
Insurance Premium ◽  
Insurance Company ◽  
Risk Of Death ◽  
Premium Price ◽  
Probability Of Death ◽  
And Gender

The price of life insurance premiums for each person depends on the probability of death, not only based on age and gender as offered by an Indonesian insurance company.  The purpose of this study is to determine premium prices on underwriting factors and frailty factors using Generalized Linear Mixed Models (GLMM). GLMM is used for modeling a combination of fixed effect heterogeneity (underwriting factors) and random effects (frailty factors) between individuals. The data used longitudinal data about underwriting factors that have Binomial distribution are taken from the Health and Retirement Study and processed using R software. Because the data used by survey data within an interval of two years, so the probability of death is obtained for an interval the next two years. Underwriting factors that have a significant effect on the probability of death are age, alcoholic status, heart disease, and diabetes. As a result, is obtained the probability of death models each individual to determine life insurance premium prices. The premium price of each individual is different because depends on underwriting factors and frailty. If frailty is positive, it means that a person level of vulnerability when experiencing the risk of death is greater than negative frailty.

scholarly journals Generalized Linear Models in Vehicle Insurance

2014 ◽  
Vol 62 (2) ◽  
pp. 383-388 ◽  
Author(s):  
Silvie Kafková ◽  
Lenka Křivánková
Keyword(s):  
Risk Factors ◽  
Linear Models ◽  
Information Criterion ◽  
Insurance Premium ◽  
Insurance Companies ◽  
Predictor Variables ◽  
Estimation Of Parameters ◽  
Claim Frequency ◽  
Insurance Data ◽  
Selection Of

Actuaries in insurance companies try to find the best model for an estimation of insurance premium. It depends on many risk factors, e.g. the car characteristics and the profile of the driver. In this paper, an analysis of the portfolio of vehicle insurance data using a generalized linear model (GLM) is performed. The main advantage of the approach presented in this article is that the GLMs are not limited by inflexible preconditions. Our aim is to predict the relation of annual claim frequency on given risk factors. Based on a large real-world sample of data from 57 410 vehicles, the present study proposed a classification analysis approach that addresses the selection of predictor variables. The models with different predictor variables are compared by analysis of deviance and Akaike information criterion (AIC). Based on this comparison, the model for the best estimate of annual claim frequency is chosen. All statistical calculations are computed in R environment, which contains stats package with the function for the estimation of parameters of GLM and the function for analysis of deviation.

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