Markov chains (MCs) are widely used to model a great deal of financial and actuarial problems. Likewise, they also in many other fields ranging from economics, management, agricultural sciences, engineering or informatics medicine. This paper focuses on the use MCs for design non-life bonus-malus systems (BMSs). It proposes quantifying uncertainty transition probabilities BMSs by using fuzzy nu...

Applications of fuzzy set theory (FST) to property casualty and life insurance have emerged in the last few years through the work of Lemaire (1990), Cummins and Derrig (1991, 1993) and Ostaszewski (1993). This paper continues that line of research by providing an overview of fuzzy pattern recognition techniques. We utilize them in clustering for risk and claim classification. The classic clust...

In an editorial in ASTIN BULLETIN, Hans Bühlmann (2002) suggests it is time to change the teaching of life insurance theory towards the real life challenges of that industry. The following note is a response to this editorial. In Bergen we have partially taught the NUMAT, or the NUMeraire based Actuarial Teaching since the beginning of the 90ties at the Norwegian School of Economics and Busines...

Conditional expected values in Markov chains are solutions to a set of associated backward differential equations, which may be ordinary or partial depending on the number of relevant state variables. This paper investigates the validity of these differential equations by locating the points of non-smoothness of the state-wise conditional expected values, and it presents a numerical method for ...

In this paper we investigate the dependence in Fréchet spaces containing mutually exclusive risks. It is shown that, under some reasonable assumptions, the safest dependence structure, in the sense of the minimal stop-loss premiums for the aggregate claims involved, is obtained with the Fréchet lower bound and precisely corresponds to the mutually exclusive risks of the Fréchet space. In that r...