NUMERICAL EVALUATION OF LOADED CREDIBILITY

An original paper, which describes techniques for estimating premiums for risks, containing a fraction (a part) of the variance of the risk as a loading on the net risk premium.esscher premium, variance premium, the linearized credibility formula.

More General Credibility Models

This communication gives some extensions of the original Bühlmann model. The paper is devoted to semi-linear credibility, where one examines functions of the random variables representing claim amounts, rather than the claim amounts themselves.contracts, unbiased estimators, structure parameters, several approximating functions, semi-linear credibility theory, unique optimal function, parameter estimation, hierarchical semi-linear credibility theory.

Semi-linear credibility results

An original paper which suggests a way of thinking for semilinear credibility theory develpment, founded on analysis of the functions of the observable random variables. This line of thought fits perfectly within the framework of the greatest accuracy credibility theory.linear functions, the transformed observations, semi-linear credibility estimators

Linearized Credibility Formula for Exponentially Weighted Squared Error Loss Function

Is an original paper, which describes techniques for estimating premiums for risks, containing a fraction (a part) of the variance of the risk as a loading on the net risk premium.the linearized credibility formula, the best risk premium – in the sense of the minimal weighted mean squared error -, variance premium

Explicit Description of the Input Data for the Program CRAC 2.0 Used in the Applications of the Credibility Theory

In this paper a brief overview of the structure and the possibilities of the program CRAC 2.0 is given. It will be shown how sectors can be determined in order to use the hierarchical model that is built into the software. Furthermore a general structure for defining insurance problems to be solved by CRAC 2.0 will be discussed. Mathematics Subject Classification: 62P05.the software package CRAC 2.0, Jewell’s hierarchical model, practical insurance problems, structure of CRAC – input.

More general credibility models

summary:This communication gives some extensions of the original Bühlmann model. The paper is devoted to semi-linear credibility, where one examines functions of the random variables representing claim amounts, rather than the claim amounts themselves. The main purpose of semi-linear credibility theory is the estimation of $\mu _0 (\theta ) = E[f_0 (X_{t+1})| \theta ]$ (the net premium for a contract with risk parameter $\theta$) by a linear combination of given functions of the observable variables: $\underline X' = (X_1, X_2, \ldots , X_t)$. So the estimators mainly considered here are linear combinations of several functions $f_1, f_2, \ldots , f_n$ of the observable random variables. The approximation to $\mu _0 (\theta )$ based on prescribed approximating functions $f_1, f_2, \ldots , f_n$ leads to the optimal non-homogeneous linearized estimator for the semi-linear credibility model. Also we discuss the case when taking $f_p = f$ for all $p$ to find the optimal function $f$. It should be noted that the approximation to $\mu _0 (\theta )$ based on a unique optimal approximating function $f$ is always better than the one in the semi-linear credibility model based on prescribed approximating functions: $f_1, f_2, \ldots , f_n$. The usefulness of the latter approximation is that it is easy to apply, since it is sufficient to know estimates for the structure parameters appearing in the credibility factors. Therefore we give some unbiased estimators for the structure parameters. For this purpose we embed the contract in a collective of contracts, all providing independent information on the structure distribution. We close this paper by giving the semi-linear hierarchical model used in the applications chapter

Credibility Models

The paper presents the mathematical theory of some credibility models, involving complicated properties of conditional expectations and conditional covariance. The fact that is based on complicated mathematics will give more insight and understanding of the theoretical aspects and will point the way to the practical possibilities of the credibility models.the risk premium, the credibility calculations

Estimation of the Credibility in the Original Bühlmann Model Illustrated by Introducing a Regression Technique

In this article we give the mathematical theory of some credibility models. The first section describes the original credibility model of Bühlmann and we derive the best linearized credibility estimator for this model. His original model, involving only one contract, contains the basics of all further credibility models. Section 2 contains a description of the Hachemeister regression model allowing for effects like inflation.linearized regression credibility premium, the original credibility model of Bühlmann

EX POST AND EX ANTE IMPACT ANALYSIS OF RESEARCH PROGRAMMES USING CMMI FRAMEWORK

In this paper, we propose a new approach for evaluating research projects and programs. According our approach, the improvement might be achieved by adopting a results-based and a project portfolio approach, and assuring a research and technology development (RTD) indicators documentation through a standard and comprehensive indicator description, named indicator template. The results-based approach will assure a consistent indicators structure, according to the results chains and a strong connection between ex ante and ex post impact evaluation. The project portfolio approach will assure a tight integration of the research performance indicators, especially between policies goals and program results. And, finally defining a comprehensive indicator template it will be possible to understand better the indicators, develop a detailed analysis, based on the business intelligence techniques, such as OLAP (On-Line Analytical Processing), data mining and text mining. According our knowledge the usage of this kind of techniques on RTD metadata is an innovative process. What we expect to find out is the indicators similarities and differentiations, the indicators clusters, the association between indicators, the most important input factors of indicators definition. According the results-based and project portfolio approach the discovered patterns will be evaluatedRDT indicator, RDT statistics, indicator template, data mining, text mining.

Estimation of the Credibility in the Original Bühlmann Model Illustrated by Introducing a Regression Technique

In this article we give the mathematical theory of some credibility models. The first section describes the original credibility model of Bühlmann and we derive the best linearized credibility estimator for this model. His original model, involving only one contract, contains the basics of all further credibility models. Section 2 contains a description of the Hachemeister regression model allowing for effects like inflation