Credibility theory and filter theory in discrete and continuous time

It is well known that credibility theory in discrete time is closely related to the discrete technique of Kalman filtering. In this paper we show the close relationship between credibility theory and filter theory in discrete and continuous time as well as between credibility theory in a discrete and continuous time setting. --

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

Credibility theory for phase-type distributions

Credibility theory provides important guidelines for insurers in the practice of experience rating. It recognizes multiple sources of risk and proposes potential premium adjustments by considering individual experiences along with the class experiences. Two popular tools in credibility theory are Bayesian and Buhlmann premium estimators. This thesis develops both models assuming a phase-type distribution of losses, following a Bayesian inference approach. A family of conjugate priors is first established accordingly. The solutions for both Bayesian and Buhlmann estimators are then obtained in explicit forms. Simulation studies are performed to evaluate each estimator individually as well as to conduct comparisons where appropriate. Mean squared errors for each estimator are computed based on different prior choices and outcomes are compared against theoretical results

Credibility Theory and Kalman Filtering with Extensions

In this paper it is shown that the estimate and prediction problems considered in credibility theory are similar to those considered in Kalman filtering theory. The state vector of the risk model consists of the average risk variables such as the number of claims, cost of claims, etc. for a particular risk from the collective of risks. The observed data consists of the risk variables for the collective and for the individual risks. It is required to predict the values of risk variables in the next time period based on this data and to adjust the individual premiums based on claims experience in such a way as to converge to their true values

The Linear Markov Property in Credibility Theory

We 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 model

An analysis of possible applications of fuzzy set theory to the actuarial credibility theory

In this work, we review the basic concepts of actuarial credibility theory from the point of view of introducing applications of the fuzzy set-theoretic method. We show how the concept of actuarial credibility can be modeled through the fuzzy set membership functions and how fuzzy set methods, especially fuzzy pattern recognition, can provide an alternative tool for estimating credibility

Credibility theory-based available transfer capability assessment

Since the development of large scale power grid interconnections and power markets, research on available transfer capability (ATC) has attracted great attention. The challenges for accurate assessment of ATC originate from the numerous uncertainties in electricity generation, transmission, distribution and utilization sectors. Power system uncertainties can be mainly described as two types: randomness and fuzziness. However, the traditional transmission reliability margin (TRM) approach only considers randomness. Based on credibility theory, this paper firstly built models of generators, transmission lines and loads according to their features of both randomness and fuzziness. Then a random fuzzy simulation is applied, along with a novel method proposed for ATC assessment, in which both randomness and fuzziness are considered. The bootstrap method and multi-core parallel computing technique are introduced to enhance the processing speed. By implementing simulation for the IEEE-30-bus system and a real-life system located in Northwest China, the viability of the models and the proposed method is verified