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.

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.

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.

1-Jet Riemann-Finsler Geometry for the Three-Dimensional Time

The aim of this paper is to develop on the 1-jet space J^1(R,M^3) the Finsler-like geometry (in the sense of distinguished (d-) connection, d-torsions and d-curvatures) of the rheonomic Berwald-Moor metric of order three. Some natural geometrical field theories (gravitational and electromagnetic) produced by the preceding rheonomic Berwald-Moor metric of order three are also exposed.Comment: 14 page

THE PRICING OF AUDIT SERVICES: EVIDENCE FROM ROMANIA

The main objective of this study is to investigate factors influencing theamount of external audit fees in Romania. Of particular interest is the examination ofthe potential effect of the client size, client complexity, and the size of the audit firmon external audit fees. An audit fee model is used to examine the effect of audit clientsize, client complexity, and the size of the audit firm on the amount of audit fees for asample of audit engagements performed in the tow of Romanian major counties. Thestudy’s results indicate that the amount of external audit fees is significantlyinfluenced by the audit client size, by the amount of turnover, by the number ofemployees. This study is original since it is the first to empirically investigate factorsinfluencing the pricing of audit services in on Romanian audit fee market.Romania, Auditor’s fees, External auditing, Auditors, Modelling

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